Dynamic Stochastic Model Research Articles

СТОХАСТИЧНЕ МОДЕЛЮВАННЯ ОПТИМАЛЬНИХ ЗВ’ЯЗКІВ МІЖ ТІНЬОВОЮ ТА ЛЕГАЛЬНОЮ ЕКОНОМІКАМИ

The article is devoted to the stochastic modelling of optimal links between the shadow and legal economies using Wiener and Poisson processes. The study focuses on identifying the best management strategies that will help reduce the size of the shadow economy. The paper first considers a deterministic economic and mathematical model of the relationship between the shadow and legal economies, which is presented in the form of differential equations with initial conditions. These differential equations describe the rate of change of real sector workers' savings, the dynamics of owners' savings, the rate of change of the price of aggregate output, etc. The assumptions about the dynamics of cash savings and the price of aggregate output are supplemented by initial conditions. Restrictions on the consumer shares of savings used for consumption of legal and shadow products for employees and entrepreneurs are formed. To build an optimal process, the author formalizes an objective function (objective criterion) that maximizes the average total (integral) savings of employees and entrepreneurs over a certain period of time and uses stochastic sufficient conditions for optimality, where the controls are the shares of savings used to purchase aggregate products of the legal and shadow economies of employees and business owners, and the phase trajectories are the monetary savings of employees and business owners of legal and shadow economies, the price of a unit of aggregate products, and the price of a unit of aggregate products. Thus, the main idea of the process of solving the optimal management problem takes into account both the management process itself (strategies, management methods) and the paths along which the system moves from the initial state to the final result (phase trajectories). The structure of the optimal process of the proposed stochastic model is described. It is established that the optimal controls are deterministic values and do not depend on the coefficients of the Wiener processes in the proposed stochastic dynamic model. It is also worth noting that the specific formulation of this problem of optimal control of the interaction between the shadow and legal economies depends on the context of the study and may vary depending on the tasks and assumptions set.

Non-equilibrium Onsager–Machlup theory

This paper proposes a simple mathematical model of non-stationary and non-linear stochastic dynamics, which approximates a (globally) non-stationary and non-linear stochastic process by its locally (or ‘piecewise’) stationary version. Profiting from the elegance and simplicity of both, the exact mathematical model referred to as the Ornstein–Uhlenbeck stochastic process (which is globally stationary, Markov and Gaussian) and of the Lyapunov criterion associated with the stability of stationarity, we show that the proposed non-linear non-stationary model provides a natural extension of the Onsager–Machlup theory of equilibrium thermal fluctuations, to the realm of non-stationary, non-linear and non-equilibrium processes. As an illustrative application, we then apply the extended non-equilibrium Onsager–Machlup theory, to the description of thermal fluctuations and irreversible relaxation processes in liquids, leading to the main exact equations employed to construct the non-equilibrium self-consistent generalised Langevin equation (NE-SCGLE) theory of irreversible processes in liquids. This generic theory has demonstrated that the most intriguing and long-unsolved questions of the glass and gel transitions are understood as a natural consequence of the second law of thermodynamics, enunciated in terms of the proposed piecewise stationary stochastic mathematical model.

Integrated optimization of facility location, casualty allocation and medical staff planning for post-disaster emergency response

PurposeDisaster management and humanitarian logistics (HT) play crucial roles in large-scale events such as earthquakes, floods, hurricanes and tsunamis. Well-organized disaster response is crucial for effectively managing medical centres, staff allocation and casualty distribution during emergencies. To address this issue, this study aims to introduce a multi-objective stochastic programming model to enhance disaster preparedness and response, focusing on the critical first 72 h after earthquakes. The purpose is to optimize the allocation of resources, temporary medical centres and medical staff to save lives effectively.Design/methodology/approachThis study uses stochastic programming-based dynamic modelling and a discrete-time Markov Chain to address uncertainty. The model considers potential road and hospital damage and distance limits and introduces an a-reliability level for untreated casualties. It divides the initial 72 h into four periods to capture earthquake dynamics.FindingsUsing a real case study in Istanbul’s Kartal district, the model’s effectiveness is demonstrated for earthquake scenarios. Key insights include optimal medical centre locations, required capacities, necessary medical staff and casualty allocation strategies, all vital for efficient disaster response within the critical first 72 h.Originality/valueThis study innovates by integrating stochastic programming and dynamic modelling to tackle post-disaster medical response. The use of a Markov Chain for uncertain health conditions and focus on the immediate aftermath of earthquakes offer practical value. By optimizing resource allocation amid uncertainties, the study contributes significantly to disaster management and HT research.

The stochastic stability and H∞‐fuzzy control of stochastic bifurcation of a doubly‐fed induction generator

AbstractConsidering the dynamic behavior of doubly‐fed induction generators (DFIGs) under the influence of random factors, this paper not only analyzes the phenomenon of stochastic instability and bifurcation of a DFIG dynamic variable in its random space when they are affected by environmental noise, but also proposes a method based on the Tkagi–Sugneo (T–S) fuzzy control strategy to control its stochastic bifurcation. First, a four‐dimensional stochastic dynamic DFIG model is established by using multiplicative white noise to simulate the influence of environmental noise on electrical variables, and stochastic central manifold theory is used to reduce the dimensionality of a planar model in the bifurcation neighborhood. Then, the stochastic stability of the model is investigated based on singular boundary theory, while the steady‐state probability density of the stochastic DFIG is determined using the Fokker–Plank–Kolmogorov equation to obtain the location and probability density of its stochastic P‐bifurcation. Finally, the influence of stochastic bifurcation behavior is eliminated by H∞‐fuzzy output feedback control. The numerical simulation results indicate that the location and probability of stochastic bifurcation in a DFIG will vary with the change in noise intensity, and the bifurcation parameter values and stochastic stability domain are obtained. The harm caused by random factors can be solved based on H∞‐fuzzy output feedback, which provides a theoretical basis for the stable operation of the DFIG system.

A Stochastic Model for Cascading Failures in Financial Networks

We study cascading failures in time-varying and uncertain financial networks. First we develop a stochastic dynamic model for the mean and covariance matrix of the market value of each company in the network. Second, we provide a steady-state analysis, we characterize equilibrium points and we provide conditions on the asymptotic stability of such points. For the covariance matrix the dynamics have the form of a Lyapunov equation and simulating such dynamics can be viewed as a numerical method to compute the steady-state solution. As a general insight, the dynamics reveal the probability of failure of each company during the transient and at steady-state. Finally, we perform a robust analysis to obtain bounding sets for the mean market value in absence of information on the covariance.

2814. The Impact of Novel Antibiotics on Curbing Antimicrobial Resistance and Infection Spread a Dynamic Modeling Study

Abstract Background Antimicrobial resistance (AMR) is a growing global concern. Novel antibiotics (ABXs) target resistant pathogens causing gram-negative (GN) bacterial infections. This study assesses the broader impact of novel ABX use on the US healthcare system, including preventing the onward spread of infections and reducing the level of high-threat AMR. Methods A stochastic dynamic transmission model was developed to simulate the interaction between infection transmissibility, bacterial resistance development, and multiple lines of ABX. Included infection types were intra-abdominal infections, urinary tract infections and hospital-acquired /ventilator-associated pneumonia. Included AMR types were carbapenem-resistant and ESBL-producing enterobacterales (CRE and ESBLE), and multi-drug resistant pseudomonas aeruginosa (MDRP). The model has compartments for non-infected, colonized, or infected patients, with a sensitive or resistant strain in a US hospital. Infected patients receive antibiotics resulting in infection clearance or use of an alternate ABX class. Sensitive pathogens gain resistance due to drug pressure or conversely could lose resistance. Ordinary differential equations were used to estimate compartment membership. The primary data source was the Premier healthcare database (172 hospitals, 2016-2020). The model examined the potential reduction in AMR levels and avoided hospital infections, by comparing two scenarios: targeted use of novel ABX for specific AMR types and the status quo with limited novel ABX use. Results When even novel ABXs are reserved as the 2nd or 3rd line of treatment, compared to the status quo, it could result in a ∼1.5% reduction in hospital infections and a change in CRE, ESBLE, and MDRP by −2.5%, −3.6%, and −2.1%, respectively, on an annual basis. The cumulative impact of novel ABXs over 5-10 years was much larger but subject to higher prediction uncertainty. The primary driver of results are infection clearance rates, risk of resistance gain on various ABX, and uptake of novel ABX. Conclusion Targeted use of novel ABXs for resistant pathogens could lead to improved, earlier infection clearance with most types of infections and pathogens, thereby reducing infection transmission and rise of high-threat AMR in the long-term. Disclosures Apoorva Ambavane, PhD, Merck & Co., Inc: Grant/Research Support Michal Litkiewicz, MSc, Merck & Co., Inc: Grant/Research Support Aditya Sardesai, MSc, CSL Seqirus: Advisor/Consultant|Merck & Co. Inc: Grant/Research Support|Merck & Co. Inc: Grant/Research Support Diana Teloian, MA, Merck & Co., Inc: Grant/Research Support Engels N. Obi, PhD, Merck & Co Inc: Employee Joe Yang, PhD, Merck & Co., Inc: Employee|Merck & Co., Inc: Stocks/Bonds

Stochastic stress response and dynamic reliability evaluation for transmission towers with semi-rigid behaviors

As a kind of typical wind-sensitive structure, transmission towers have attracted fast-growing attention in the field of their wind-induced dynamic response. Nevertheless, their dynamic response considering effects of semi-rigid connected joints and semi-rigid-constrained stability behaviors has not been investigated. To this end, based on the experimental and numerical study, this paper proposes a fitting formula for the stability coefficient of steel tube members with semi-rigid behaviors in transmission towers to determine the dynamic stress response. Then, the stiffness, mass, and damping matrices of steel-tube transmission towers (STTTs) with semi-rigid behaviors are determined to construct their stochastic dynamic finite element model. Subsequently, the integral form of the generalized density evolution equation is solved via a family of Dirac's sequences to conduct the stochastic stress response analysis for STTTs considering effects of semi-rigid connected joints and semi-rigid-constrained stability behaviors, and their dynamic reliability is evaluated by further introducing the extreme-value distribution method. Finally, an engineering example of an existing STTT is given, and the results indicate that the semi-rigid connected joints and semi-rigid-constrained stability behaviors would significantly affect the stochastic stress response and dynamic reliability of STTTs. Accordingly, taking into account semi-rigid connected joints and semi-rigid-constrained stability behaviors may be more applicable for analysis and design of STTTs.

A Dynamic Spatiotemporal Stochastic Volatility Model with an Application to Environmental Risks

A dynamic spatiotemporal stochastic volatility (SV) model is introduced, incorporating explicit terms accounting for spatial, temporal, and spatiotemporal spillover effects. Alongside these features, the model encompasses time-invariant site-specific factors, allowing for differentiation in volatility levels across locations. The statistical properties of an outcome variable within this model framework are examined, revealing the induction of spatial dependence in the outcome variable. Additionally, a Bayesian estimation procedure employing the Markov Chain Monte Carlo (MCMC) approach, complemented by a suitable data transformation, is presented. Simulation experiments are conducted to assess the performance of the proposed Bayesian estimator. Subsequently, the model is applied in the domain of environmental risk modeling, addressing the scarcity of empirical studies in this field. The significance of climate variation studies is emphasized, illustrated by an analysis of local air quality in Northern Italy during 2021, which underscores pronounced spatial and temporal clusters and increased uncertainties/risks during the winter season compared to the summer season.

Identification of a Stochastic Dynamic Model for Aircraft Flight Attitude Based on Measured Data

Stochastic disturbances are everywhere. The influence of stochastic factors on the modeling and simulation of aircraft flight dynamics should be considered. Therefore, a stochastic differential equation for aircraft flight attitude is modeled based on the traditional one in this paper. After that, an identification method based on the idea of sparse recognition for unknown parameters and stochastic disturbance is proposed. Finally, a set of measured flight data is used to verify that the identified stochastic model has obvious advantages over the traditional deterministic model when the aircraft is maneuvering in flight. This method can improve the accuracy and reliability of the aircraft flight dynamic model.

A stochastic dynamic network loading model for mixed traffic with autonomous and human-driven vehicles

In this study, we develop a stochastic dynamic network loading (DNL) model for the mixed traffic with autonomous vehicles (AVs) and human-driven vehicles (HVs). The source of stochasticity is the uncertainty inherent in the arrival process of the two classes of vehicular flow. The developed model captures both within-link and between-link traffic flow dependencies and evaluates the network state distribution in an analytical manner. The model has two main components, a probabilistic link model and a probabilistic node model. The link model is a stochastic formulation of the link transmission model (LTM), which captures the boundary conditions of a link and approximates the evolution of link state distribution. The node model, on the other hand, characterizes the flow transmissions across a network node. It reflects the between-link dependency by evaluating the expected transmission flow through an iterative algorithm, with an explicit consideration of the interactions between supply and demand constraints associated with a node. The developed model is validated versus replicated running of the deterministic LTM as well as microscopic traffic simulations, and the results reveal that it yields relatively accurate estimations. We also present two applications of the proposed model, including a traffic signal control problem and a class-based ramp metering problem, to demonstrate its practical value.

Universal abundance fluctuations across microbial communities, tropical forests, and urban populations.

The growth of complex populations, such as microbial communities, forests, and cities, occurs over vastly different spatial and temporal scales. Although research in different fields has developed detailed, system-specific models to understand each individual system, a unified analysis of different complex populations is lacking; such an analysis could deepen our understanding of each system and facilitate cross-pollination of tools and insights across fields. Here, we use a shared framework to analyze time-series data of the human gut microbiome, tropical forest, and urban employment. We demonstrate that a single, three-parameter model of stochastic population dynamics can reproduce the empirical distributions of population abundances and fluctuations in all three datasets. The three parameters characterizing a species measure its mean abundance, deterministic stability, and stochasticity. Our analysis reveals that, despite the vast differences in scale, all three systems occupy a similar region of parameter space when time is measured in generations. In other words, although the fluctuations observed in these systems may appear different, this difference is primarily due to the different physical timescales associated with each system. Further, we show that the distribution of temporal abundance fluctuations is described by just two parameters and derive a two-parameter functional form for abundance fluctuations to improve risk estimation and forecasting.

Sustainable ecosystem management based on optimal water allocation and equity measures

Abstract Allocation of water resources is an interesting research topic and one of the main challenges of arid regions. From the point of view of agriculture, this issue is closely related to ecological balance, economic development and social stability. Therefore, fair, efficient and sustainable allocation of water resources for users and decision-making is essential. This paper presents a dynamic stochastic programming model that predicts soil moisture content in a growing season based on data collected from an experimental farm. The model included three types of loam soil, silt loam and clay loam with three treatments of irrigation intervals of 3, 7, 10 and 14 days and three amounts of water allocation with three replications. The proposed framework was evaluated with two criteria of spatial and temporal equity, and the optimal water allocation was analyzed based on this criterion. The results showed that the criterion of temporal equity for loam soil with 7-day irrigation intervals is more than twice that of 14-day irrigation intervals. In addition, the depth of irrigation has had the greatest impact on the fluctuations of the criterion of equity in water allocation in the growing season.

Stochastic model for cell population dynamics quantifies homeostasis in colonic crypts and its disruption in early tumorigenesis.

The questions of how healthy colonic crypts maintain their size, and how homeostasis is disrupted by driver mutations, are central to understanding colorectal tumorigenesis. We propose a three-type stochastic branching process, which accounts for stem, transit-amplifying (TA) and fully differentiated (FD) cells, to model the dynamics of cell populations residing in colonic crypts. Our model is simple in its formulation, allowing us to estimate all but one of the model parameters from the literature. Fitting the single remaining parameter, we find that model results agree well with data from healthy human colonic crypts, capturing the considerable variance in population sizes observed experimentally. Importantly, our model predicts a steady-state population in healthy colonic crypts for relevant parameter values. We show that APC and KRAS mutations, the most significant early alterations leading to colorectal cancer, result in increased steady-state populations in mutated crypts, in agreement with experimental results. Finally, our model predicts a simple condition for unbounded growth of cells in a crypt, corresponding to colorectal malignancy. This is predicted to occur when the division rate of TA cells exceeds their differentiation rate, with implications for therapeutic cancer prevention strategies.

Data-driven modelling and dynamic analysis of the multistable energy harvester with non-Gaussian Lévy noise

In engineering, due to the complex structural characteristics of system and the non-Gaussian properties of random excitation, it is difficult to establish an accurate stochastic dynamic model for the strongly nonlinear multistable vibration energy harvester (VEH), especially for these driven by non-Gaussian Lévy noise. From the view of machine learning, a data-driven model identification method is devised to extract the non-Gaussian governing laws of the multistable VEH with the aid of the observed sample trajectory data. Based on the Nonlocal Kramers-Moyal formulas, the Lévy, drift and diffusion terms can be approximately expressed by the sample trajectories of the system. By implementing the least square method and the stepwise sparse regressor algorithm, the optimal drift and diffusion coefficients can be identified, and then the non-Gaussian stochastic differential equation of VEH is extracted. Two examples are utilized to verify the feasibility and effectiveness of the data-driven modelling method in VEH, which indicates that the identified results agree well with the original system. Finally, the stochastic dynamic behaviors induced by non-Gaussian Lévy noise are explored based on the data-driven penta-stable VEH. The proposed method can provide the theoretical guidance for the modelling and dynamics research of VEH in engineering.

Ferry Scheduling Optimization Considering Arrival Time Uncertainty and In-Place Time Differences

The aircraft ferry service is an important link in the transfer of travelers between the remote parking stand and the terminal. By analyzing the process of inbound and outbound ferry service, the relationship between the in-place time of each ferry on the same flight is clarified. A ferry service splitting method considering the difference in in-place time is proposed. Based on this, a dynamic programming scheduling model for ferries is innovatively developed. Considering the impact of flight arrival and departure uncertainty on the in-place time of ferry service, the model is transformed into a dynamic programming stochastic model with opportunity constraints. The optimization objective of this model is to minimize the number of ferries used. To describe the model more easily, a sample average approximation technique is introduced to transform the stochastic model into a deterministic model with confidence. A genetic algorithm based on Monte Carlo random sampling is designed to solve the model. The experimental results based on the actual operation data of an airport in South China show that the dynamic splitting method considering the difference in the in-place time of the ferry can improve the resource utilization efficiency; the scheduling scheme based on the dynamic planning stochastic model has better robustness.

An Empirical noise model of centrifugal fans with different volute tongues based on Langevin regression

In the context of the rapidly evolving field of building ventilation, fan noise control stands out as a pivotal technology to enhance the quality of life. This study aimed to elucidate the inherent randomness, distinct characteristics, and potential low-dimensional noise structure essential for developing effective noise control methods. In this study, a stochastic dynamics model for the noise of centrifugal fans with various volute tongue structures is constructed using the Langevin regression method and experimental measurements. An empirical noise model capturing the peak characteristics of noise discrete tonal is developed through parametric mode expansion and an empirical mean-field model of turbulent wakes, facilitating accurate noise predictions. The research findings demonstrate the effectiveness of the Langevin equation employing the cubic Stuart-Landau equation and multiplicative noise to predict fan noise across different volute tongue structures. While stochastic dynamics models unavoidably lose the characteristic discrete noise peaks, predictions of the total A-weighted sound pressure level remain within a 2.2% error margin. The stochastic dynamics models applied to centrifugal fan aerodynamic noise and turbulent wakes exhibit striking resemblances, suggesting a fundamental connection between turbulence and noise generation. The extended empirical noise model maintains discrete pitch noise peaks by introducing shift modes, indicating that stronger Langevin deformations correspond to larger translational amplitudes of the shift modes. The advancement of stochastic dynamics and empirical noise models lays a foundational framework for the formulation of effective noise control strategies.

Stochastic Dynamical Modeling of Wind Farm Turbulence

Low-fidelity engineering wake models are often combined with linear superposition laws to predict wake velocities across wind farms under steady atmospheric conditions. While convenient for wind farm planning and long-term performance evaluation, such models are unable to capture the time-varying nature of the waked velocity field, as they are agnostic to the complex aerodynamic interactions among wind turbines and the effects of atmospheric boundary layer turbulence. To account for such effects while remaining amenable to conventional system-theoretic tools for flow estimation and control, we propose a new class of data-enhanced physics-based models for the dynamics of wind farm flow fluctuations. Our approach relies on the predictive capability of the stochastically forced linearized Navier–Stokes equations around static base flow profiles provided by conventional engineering wake models. We identify the stochastic forcing into the linearized dynamics via convex optimization to ensure statistical consistency with higher-fidelity models or experimental measurements while preserving model parsimony. We demonstrate the utility of our approach in completing the statistical signature of wake turbulence in accordance with large-eddy simulations of turbulent flow over a cascade of yawed wind turbines. Our numerical experiments provide insight into the significance of spatially distributed field measurements in recovering the statistical signature of wind farm turbulence and training stochastic linear models for short-term wind forecasting.

Stochastic analysis of air–sea heat fluxes variability in the North Atlantic in 1979–2022 based on reanalysis data

A dynamic stochastic model based on the Langevin stochastic differential equation is introduced for the reanalysis data of the ERA5 database to model and analyze the behavior of latent and sensible air–sea heat fluxes in the North Atlantic for the period 1979–2022. The point estimates of the random coefficients (the drift vector and the diffusion matrix) of this type of equation for the entire period under consideration are presented. The numerical methods and software tools for statistical analysis of time evolution of the coefficients as well as determination their relationships and the behavior of their maxima, averages and minima at various time intervals (days, months, years), are developed. A strong seasonality for the coefficients of the equation is demonstrated. The spatiotemporal variability of the dynamic and stochastic components of the coefficients of the Langevin equation and their relationship with jet streams of different regions of the North Atlantic is analyzed. The presence of non-trivial positive trends in the drift and diffusion coefficients, especially for the latent fluxes, within the interannual variability is demonstrated. One indicates a quantitative increase in the air–sea interaction on the interannual scale. Numerical estimation was carried out using high-performance computing cluster with software implementation in the Python programming language. The tools for dynamic visualization of various quantities on geographical maps of the region under consideration are also presented.

Evaluating the effectiveness of monetary policy for retail central bank digital currency

This paper evaluates the macroeconomic effects of monetary policy for a central bank digital currency rule with traditional monetary policy in an open environment. We build a dynamic stochastic general equilibrium small open model economy with interest-bearing central bank digital currency assets. The redistribution of asset holdings and the change in asset price are the two pathways through which a retail central bank digital currency rule under the traditional monetary policy affects the macroeconomy. Fiat's digital and traditional monetary policies complement one another in lowering macroeconomic fluctuations. As a result, the real exchange rate, current accounts, and consumption are more stable in transmitting foreign shocks. These results occur when price-based or quantitative-based fiat digital monetary policy parallels traditional price-based monetary policy.

Dynamic analysis of healthcare providers’ cost efficiency

ABSTRACT This study uses quarterly longitudinal data to examine the cost efficiency of 20 New Zealand District Health Boards between 2011 and 2018. A random-effects dynamic stochastic frontier model is applied to estimate the persistence of Health Boards’ cost efficiency while considering both observed and unobserved heterogeneity. The findings reveal that New Zealand Health Boards, on average, spent approximately 7.5% more than the estimated costs of efficient operation, primarily due to high persistence in cost inefficiency. Notably, Health Boards serving rural areas faced even higher levels of long-run cost inefficiency, resulting in an overspending of about 15% of annual budgets. The results of this study highlight that most Health Boards demonstrated excellent short-term performance relative to the long-run equilibrium level of cost inefficiency. However, the more significant concern lies in high long-run cost inefficiency within the sector attributed to structural and regulatory issues. Policymakers are urged to address these underlying problems to improve overall cost efficiency in the health sector.