Stochastic Model Research Articles

Comprehensive Analysis of Deterministic and Stochastic Eco-Epidemic Models Incorporating Fear, Refuge, Supplementary Resources, and Selective Predation Effects

Comprehensive Analysis of Deterministic and Stochastic Eco-Epidemic Models Incorporating Fear, Refuge, Supplementary Resources, and Selective Predation Effects

Measuring productivity when technology is heterogeneous using a latent class stochastic frontier model

Measuring productivity when technology is heterogeneous using a latent class stochastic frontier model

A Deterministic and Stochastic Fractional-Order ILSR Rumor Propagation Model Incorporating Media Reports and a Nonlinear Inhibition Mechanism

A Deterministic and Stochastic Fractional-Order ILSR Rumor Propagation Model Incorporating Media Reports and a Nonlinear Inhibition Mechanism

A stochastic modelling framework for predicting flexural properties of ultra-thin randomly oriented strands

A stochastic modelling framework is developed to predict the flexural properties of high-strength sheet moulding compounds made of randomly oriented ultra-thin carbon fibre-reinforced thermoplastic prepreg tapes. The model enables reliable designs using ultra-thin randomly oriented strands with less testing, leading to potential applications in automotive primary structures. The stochastic model is based on a Monte Carlo simulation. The flexural modulus is predicted using classical laminate theory, while the flexural strength is predicted by following a Weibull distribution. Fibre discontinuities are considered through stress concentrations introduced by tape overlaps. The results are validated against new 3-point bending and previously reported 4-point bending experimental results. A scaling effect on strength and scatter is predicted, and its implications for structural applications are also discussed.

Adaptive Design of Solar-Powered Energy Systems Based on Daily Clearness State Evolution

The optimal designing of the hybrid energy system (HES) is a challenging task due to the multiple objectives and various uncertainties. Especially for HES, primarily powered by solar energy, the reference solar radiation data directly impact the result of the optimization design. To incorporate the stochastic characteristics of solar radiation into the sizing process, a data-driven stochastic modeling method for solar radiation is proposed. The method involves two layers of stochastic processes that capture the intraday variation and daily evolution of solar radiation. First, the clearness index (CI) is introduced to describe the radiation intensity at different times. Then, the daily clearness state (DCS) is proposed, based on the statistical indicators of the intraday CI. The Markov model is used to describe the stochastic evolutionary characteristics between different DCSs. The probabilistic distribution of the CI under different DCS is obtained based on the diffusion kernel density estimation (DKDE), which is used for the stochastic generation of the CI at various times of the day. Finally, the radiation profile required for the optimal design is obtained by the stochastic generation of the DCS sequences and the intraday clearness index under corresponding states. A case study of an off-grid solar-powered HES is provided to illustrate this methodology.

Decision Analysis of Cold Chain Supply Chain Based on a Stochastic Evolution Model

Accelerating the development of cold chain logistics for agricultural products is not only an objective requirement for the development of agricultural product circulation but also a necessary demand to promote rural revitalization and upgrade agricultural consumption. Addressing the evolutionary problems of cold chain transportation in uncertain environments, this study considers the actual stochastic disturbances in the cold chain supply chain system, introducing Gaussian white noise to reflect the random perturbations experienced during the evolution of the cold chain. A three-party stochastic evolutionary game model is established involving farmers, logistics enterprises, and government regulatory authorities. Based on this model, numerical simulation analysis is conducted to explore the effects of different factors such as the intensity of random disturbances and the loss transfer coefficient on the fluctuation of strategic choices of the entities and the convergence speed to a stable state during evolution. Finally, combining the results of numerical simulation, relevant policies and recommendations are proposed to provide insights and guidance for the development of cold chain logistics in agricultural products.

Asymptotic predictions on the velocity gradient statistics in low-Reynolds-number random flows: onset of skewness, intermittency and alignments

Stirring a fluid through a Gaussian forcing at a vanishingly small Reynolds number produces a Gaussian random field, while flows at higher Reynolds numbers exhibit non-Gaussianity, cascades, anomalous scaling and preferential alignments. Recent works (Yakhot & Donzis, Phys. Rev. Lett., vol. 119, 2017, 044501; Khurshid et al., Phys. Rev. E, vol. 107, 2023, 045102) investigated the onset of these turbulent hallmarks in low-Reynolds-number flows by focusing on the scaling of the velocity gradients and velocity increments. They showed that the onset of power-law scalings in the velocity gradient statistics occurs at low Reynolds numbers, with the scaling exponents being surprisingly similar to those in the inertial range of fully developed turbulence. In this work we address the onset of turbulent signatures in low-Reynolds-number flows from the viewpoint of the velocity gradient dynamics, giving insights into its rich statistical geometry. We combine a perturbation theory of the full Navier–Stokes equations with velocity gradient modelling. This procedure results in a stochastic model for the velocity gradient in which the model coefficients follow directly from the Navier–Stokes equations and statistical homogeneity constraints. The Fokker–Planck equation associated with our stochastic model admits an analytic solution that shows the onset of turbulent hallmarks at low Reynolds numbers: skewness, intermittency and preferential alignments arise in the velocity gradient statistics through a smooth transition as the Reynolds number increases. The model predictions are in excellent agreement with direct numerical simulations of low-Reynolds-number flows.

Optimal Scheme Models with Two Kinds of Errors

In this paper, we propose stochastic scheme models with two kinds of errors for a computer system. A highly reliable computer system needs greatly to be backed up successfully in case of computer system crashes due to hardware failures and malicious software infections. We aim to determine appropriate backup times in computer processing of constant and random tasks. For this purpose, the trade-off between backup times and data losses due to errors is considered. The total execution times until the computing processing completes are obtained, and optimal backup policies to minimize them are derived analytically. Furthermore, we take up extended models of random tasks with [Formula: see text] sub-tasks and analyze them.

Illustrating the importance of edge constraints in backbones of bipartite projections.

Bipartite projections (e.g., event co-attendance) are often used to measure unipartite networks of interest (e.g., social interaction). Backbone extraction models can be useful for reducing the noise inherent in bipartite projections. However, these models typically assume that the bipartite edges (e.g., who attended which event) are unconstrained, which may not be true in practice (e.g., a person cannot attend an event held prior to their birth). We illustrate the importance of correctly modeling such edge constraints when extracting backbones, using both synthetic data that varies the number and type of constraints, and empirical data on children's play groups. We find that failing to impose relevant constraints when the data contain constrained edges can result in the extraction of an inaccurate backbone. Therefore, we recommend that when bipartite data contain constrained edges, backbones be extracted using a model such as the Stochastic Degree Sequence Model with Edge Constraints (SDSM-EC).

Multi-Input data ASsembly for joint Analysis (MIASA): A framework for the joint analysis of disjoint sets of variables.

The joint analysis of two datasets [Formula: see text] and [Formula: see text] that describe the same phenomena (e.g. the cellular state), but measure disjoint sets of variables (e.g. mRNA vs. protein levels) is currently challenging. Traditional methods typically analyze single interaction patterns such as variance or covariance. However, problem-tailored external knowledge may contain multiple different information about the interaction between the measured variables. We introduce MIASA, a holistic framework for the joint analysis of multiple different variables. It consists of assembling multiple different information such as similarity vs. association, expressed in terms of interaction-scores or distances, for subsequent clustering/classification. In addition, our framework includes a novel qualitative Euclidean embedding method (qEE-Transition) which enables using Euclidean-distance/vector-based clustering/classification methods on datasets that have a non-Euclidean-based interaction structure. As an alternative to conventional optimization-based multidimensional scaling methods which are prone to uncertainties, our qEE-Transition generates a new vector representation for each element of the dataset union [Formula: see text] in a common Euclidean space while strictly preserving the original ordering of the assembled interaction-distances. To demonstrate our work, we applied the framework to three types of simulated datasets: samples from families of distributions, samples from correlated random variables, and time-courses of statistical moments for three different types of stochastic two-gene interaction models. We then compared different clustering methods with vs. without the qEE-Transition. For all examples, we found that the qEE-Transition followed by Ward clustering had superior performance compared to non-agglomerative clustering methods but had a varied performance against ultrametric-based agglomerative methods. We also tested the qEE-Transition followed by supervised and unsupervised machine learning methods and found promising results, however, more work is needed for optimal parametrization of these methods. As a future perspective, our framework points to the importance of more developments and validation of distance-distribution models aiming to capture multiple-complex interactions between different variables.

Some New Results on Stochastic Comparisons of Spacings of Generalized Order Statistics from One and Two Samples

Generalized order statistics (GOSs) are often adopted as a tool for providing a unified approach to several stochastic models dealing with ordered random variables. In this contribution, we first recall various useful results based on the notion of total positivity. Then, some stochastic comparisons between spacings of GOSs from one sample, as well as two samples, are developed under the more general assumptions on the parameters of the model. Specifically, the given results deal with the likelihood ratio order, the hazard rate order and the mean residual life order. Finally, an application is demonstrated for sequential systems.

Dynamic Analysis of the Bolted Joint Structure with Interval Uncertainties

This paper investigates the dynamic influence of joint interfaces in bolted joint structures subjected to uncertain-but-bounded parameters. Firstly, applying the thin layer elements (TLE) represents the contact interfaces with nonuniform stiffness distribution. The stochastic model updating method is employed to identify the uncertain parameters of TLE. Secondly, the Legendre interval method (LIM) is applied to calculate the natural frequencies of bolted lap joints with uncertain parameters. By introducing the elastic modulus of TLE as interval vectors, relations between the natural frequencies and uncertain parameters could be analyzed using the LIM. Furthermore, the dependence of the dynamic response on TLE parameters can be established based on the modal superposition principle. Considering the influence of uncertain parameters, an uncertain acceleration frequency response surrogate function (UAFRSF) is proposed to predict the dynamic behavior and qualitatively analyze the parameter sensitivity of the bolted lap joints. The elastic modulus of TLE in different contact regions is selected as the interval variable. The acceleration frequency responses of the bolted lap joints under uncertain parameters are investigated. Compared with MCs simulations with 200 samples and Chebyshev interval method results, the effectiveness of the proposed method for solving the uncertain acceleration frequency response of bolted lap joints is verified. This research will provide theoretical support for improving the design of aero-engine joint structures.

A multistage forecasting model for green bond cost optimization with dynamic corporate risk constraints

AbstractThis study develops a multi‐stage stochastic model to forecast the issuance of green bonds using the Filtered Historical Simulation (FHS) method to identify the most cost‐effective conditions for issuing these bonds amid various risk factors. Drawing on historical yield data and financial metrics of corporate green bonds from December 2014 to June 2023, the model considers fluctuating elements such as risk probabilities, financial risks in worst‐case scenarios, and liquidity risks at upcoming issuance moments. Our findings reveal the model's effectiveness in pinpointing the lowest possible costs of issuing new green bond portfolios in the future, while also addressing expected financial risk, risk occurrence probability, and liquidity issues. The results provide issuers with the insights needed to accurately time the market, tailor bond maturities according to a corporation's future risk profile, and enhance liquidity management. Notably, our model indicates that refining the estimated probability of future risk occurrences can lead to significant savings in green bond issuance costs. This approach allows for adaptable bond issuance strategies, addresses inherent debt, and enables detailed risk management, offering substantial benefits for green enterprises navigating the complexities of future financial landscapes.

A self-regulated stochastic acceleration model of pulsar wind nebulae

Abstract Pulsar wind nebulae (PWNe) are clouds of the magnetized relativistic electron/positron plasma supplied from the central pulsar. However, the number of radio-emitting particles inside a PWN is larger than the expectation from the study of pulsar magnetospheres and then their origin is still unclear. A stochastic acceleration of externally injected particles by a turbulence inside the PWN is proposed by our previous studies. In this paper, the previous stochastic acceleration model of the PWN broadband spectra is improved by taking into account the time evolution of the turbulent energy and then the total energy balance inside a PWN is maintained. The turbulent energy supplied from the central pulsar is wasted by the backreaction from the stochastic particle acceleration and the adiabatic cooling according the PWN expansion. The model is applied to the Crab Nebula and reproduce the current broadband emission spectrum, especially the flat radio spectrum although time evolution of the turbulent energy (diffusion coefficient) is a bit complicated compared with our previous studies, where we assumed an exponential behavior of the diffusion coefficient.

Examining the social and behavioral dynamics of substance use in a longitudinal network study in rural Appalachia

BackgroundPrior studies have shown that individuals and their peers often have similar substance use behaviors, but the mechanisms driving these similarities – particularly in rural settings, are not well understood. The primary objectives of this analysis are to (1) identify factors that contribute to relationship turnover and maintenance within a rural network of persons who use drugs (PWUD), (2) determine whether assimilation and/or homophily shape participants use of injection drugs, heroin, and stimulants (methamphetamine and cocaine), and (3) assess the extent that these mechanisms influence networks ties and/or behaviors and whether these effects vary across time. MethodsSociometric network data were collected from a cohort of PWUD in rural Eastern Kentucky at baseline (2008–2010) and at four follow-up visits conducted approximately semiannually. Stochastic actor-oriented models (SAOMS) were used to model network structure and participant behaviors as jointly dependent variables and to identify characteristics associated with the maintenance, dissolution, and formation of network ties and changes in drug use behaviors. ResultsFindings suggest (1) greater network stability over time for reciprocal and transitive relationships, (2) both homophily and assimilation played a greater role in shaping injection drug use (IDU) initiation and cessation than they did in shaping heroin and stimulant use, and (3) the importance of these mechanisms appeared consistent over time. ConclusionGiven the stability of particular network structures and evidence of both homophily and assimilation with respect to drug-use behaviors, interventions that leverage social networks could be used to motivate health-promoting behaviors.

A probabilistic fatigue life assessment method for wind turbine blade based on Bayesian GPR with the effects of pitch angle

AbstractThe fatigue behavior of large wind turbine blades is complex and stochastic due to their complex structure and operating environment. This paper focuses on developing a probabilistic fatigue life assessment method for wind turbine blades considering the uncertainties from wind velocity, material mechanical properties, pitch angle, and layer thickness. To improve the efficiency of stochastic fatigue behavior analysis of wind turbine blade, unidirectional fluid‐structure coupling (UFSC) and bidirectional fluid‐structure coupling (BFSC) analysis are employed to analyze the stochastic response. Then, Gaussian process regression (GPR) and Bayesian updating are combined to establish the stochastic fatigue behavior prediction model for wind turbine blade. On this basis, a modified S‐N curve formulation is proposed, and the fatigue life of wind turbine blade is analyzed by the modified S‐N curve and compared with the three‐parameter Weibull model. The results indicate that the proposed method for fatigue life assessment has better accuracy. The proposed probabilistic fatigue life assessment method with high accuracy and high efficiency, which is beneficial for the fatigue reliability design of wind turbine blades.

Economic and financial viability of a pig farm in central semi-tropical Mexico: 2022–2026 prospective

To estimate the economic and financial viability of a pig farm in central sub-tropical Mexico within a 5-year planning horizon, a Monte Carlo simulation model was utilized. Net returns were projected using simulated values for the distribution of input and product processes, establishing 2021 as base scenario. A stochastic modelling approach was employed to determine the economic and financial outlook. The findings reveal a panorama of economic and financial viability. Net income increased by 555%, return on assets rose from 3.36% in 2022 to 11.34% in 2026, and the probability of decapitalization dropped from 58% to 13%, respectively in the aforesaid periods. Similarly, the probability of obtaining negative net income decreased from 40% in 2022 to 18% in 2026. The technological, productive, and economic management of the production unit allowed for a favorable scenario within the planning horizon. There is a growing interest in predicting the economic sectors worth investing in and supporting, considering their economic and development performance. This research offers both methodological and scientific evidence to demonstrate the feasibility of establishing a planning schedule and validating the suitability of the pork sector for public investment and support.

Dynamic serviceability and safety reliability analysis of aging PC girder bridges with non-prestressed reinforcement considering concrete shrinkage, creep and stochastic vehicle load flows

Prestressed concrete (PC) bridges’ service performance displays time-dependency due to several factors including concrete shrinkage, creep, resistance degradation, and stochastic vehicle load flows. These non-stationary vehicle load flows, combined with concrete shrinkage, creep, and resistance degradation, result in sequential alterations of internal forces and deformations in simply supported PC girder bridges, ultimately influencing their dynamic reliability. This study proposes a robust methodology that considers the impact of traffic loading, shrinkage, and creep to analyze the dynamic reliability of simply supported PC girder bridges through the development of a load probability model. A stochastic model for truck loads is generated using motion measurement data, which can be used to calculate bridge internal forces and subsequent quantitative analysis of structural deformation due to shrinkage and creep. Subsequently, the formula for the first exceedance probability under resistance degradation is presented and validated through Monte Carlo simulation. Reliability analysis is conducted for both serviceability and load carrying capacity limit states to assess the impact of shrinkage, creep, and increased mean vehicle load on structural reliability. The proposed method offers the theoretical foundation and practical guidance for assessing the structural health status of in-service bridges, thereby providing valuable insights into their long-term performance and maintenance requirements.

Forward Starting Option Pricing under Double Fractional Stochastic Volatilities and Jumps

This paper aims to provide an effective method for pricing forward starting options under the double fractional stochastic volatilities mixed-exponential jump-diffusion model. The value of a forward starting option is expressed in terms of the expectation of the forward characteristic function of log return. To obtain the forward characteristic function, we approximate the pricing model with a semimartingale by introducing two small perturbed parameters. Then, we rewrite the forward characteristic function as a conditional expectation of the proportion characteristic function which is expressed in terms of the solution to a classic PDE. With the affine structure of the approximate model, we obtain the solution to the PDE. Based on the derived forward characteristic function and the Fourier transform technique, we develop a pricing algorithm for forward starting options. For comparison, we also develop a simulation scheme for evaluating forward starting options. The numerical results demonstrate that the proposed pricing algorithm is effective. Exhaustive comparative experiments on eight models show that the effects of fractional Brownian motion, mixed-exponential jump, and the second volatility component on forward starting option prices are significant, and especially, the second fractional volatility is necessary to price accurately forward starting options under the framework of fractional Brownian motion.

Estimating Markov Chain Mixing Times: Convergence Rate Towards Equilibrium of a Stochastic Process Traffic Assignment Model

Network equilibrium models have been extensively used for decades. The rationale for using equilibrium as a predictor is essentially that (i) a unique and globally stable equilibrium point is guaranteed to exist and (ii) the transient period over which a system adapts to a change is sufficiently short in time that it can be neglected. However, we find transport problems without a unique and stable equilibrium in the literature. Even if it exists, it is not certain how long it takes for the system to reach an equilibrium point after an external shock onto the transport system, such as infrastructure improvement and damage by a disaster. The day-to-day adjustment process must be analysed to answer these questions. Among several models, the Markov chain approach has been claimed to be the most general and flexible. It is also advantageous as a unique stationary distribution is guaranteed in mild conditions, even when a unique and stable equilibrium does not exist. In the present paper, we first aim to develop a methodology for estimating the Markov chain mixing time (MCMT), a worst-case assessment of the convergence time of a Markov chain to its stationary distribution. The main tools are coupling and aggregation, which enable us to analyse MCMTs in large-scale transport systems. Our second aim is to conduct a preliminary examination of the relationships between MCMTs and critical properties of the system, such as travellers’ sensitivity to differences in travel cost and the frequency of travellers’ revisions of their choices. Through analytical and numerical analyses, we found key relationships in a few transport problems, including those without a unique and stable equilibrium. We also showed that the proposed method, combined with coupling and aggregation, can be applied to larger transport models. History: This paper has been accepted for the Transportation Science Special Issue on the 25th International Symposium on Transportation and Traffic Theory. Funding: This study was financially supported by the Japan Society for the Promotion of Science [Grant-in-Aid 20H00265]. Supplemental Material: The online appendices are available at https://doi.org/10.1287/trsc.2024.0523 .