Dynamic Stochastic Model Research Articles

Detecting bubbles in Bitcoin price dynamics via market exuberance

Empirical evidence suggests the presence of bubble effects on Bitcoin price dynamics during its lifetime, starting in 2009. Previous research, mostly empirical, focused on statistical tests in order to detect a bubble behavior at some point in time. Few exceptions suggested specific time series models capable to describe such phenomena. We contribute this stream of literature by considering a continuous time stochastic model for Bitcoin dynamics, depending on a market attention factor, which is proven to boost in a bubble under suitable conditions. Here, we define a bubble following the theory of mathematical bubbles introduced by Philip E. Protter and coauthors. Specifically, we prove that the presence of a bubble is related to the correlation between the market attention factor on Bitcoin and Bitcoin returns being above a threshold, i.e. when marked attention affects Bitcoin prices and converse, creating a vicious loop. This phenomenon has been labelled market exuberance by Robert J. Shiller, recipient of the 2013 Nobel prize in Economic Sciences. The model is fitted on historical data of Bitcoin prices, by considering either the total trading volume or the Google Search Volume Index as proxies for the attention measure. According to our numerical results, a bubble effect is evidenced in the early years of Bitcoin introduction, namely 2012–2013, as well as in the recent race of 2017.

Complementing CO<sub>2</sub> emission reduction by solar radiation management might strongly enhance future welfare

Abstract. Solar radiation management (SRM) has been proposed as a means to reduce global warming in spite of high greenhouse-gas concentrations and to lower the chance of warming-induced tipping points. However, SRM may cause economic damages and its feasibility is still uncertain. To investigate the trade-off between these (economic) gains and damages, we incorporate SRM into a stochastic dynamic integrated assessment model and perform the first rigorous cost–benefit analysis of sulfate-based SRM under uncertainty, treating warming-induced climate tipping and SRM failure as stochastic elements. We find that within our model, SRM has the potential to greatly enhance future welfare and merits being taken seriously as a policy option. However, if only SRM and no CO2 abatement is used, global warming is not stabilised and will exceed 2 K. Therefore, even if successful, SRM can not replace but only complement CO2 abatement. The optimal policy combines CO2 abatement and modest SRM and succeeds in keeping global warming below 2 K.

Absorbing phase transition in the coupled dynamics of node and link states in random networks

We present a stochastic dynamics model of coupled evolution for the binary states of nodes and links in a complex network. In the context of opinion formation node states represent two possible opinions and link states represent positive or negative relationships. Dynamics proceeds via node and link state update towards pairwise satisfactory relations in which nodes in the same state are connected by positive links or nodes in different states are connected by negative links. By a mean-field rate equations analysis and Monte Carlo simulations in random networks we find an absorbing phase transition from a dynamically active phase to an absorbing phase. The transition occurs for a critical value of the relative time scale for node and link state updates. In the absorbing phase the order parameter, measuring global order, approaches exponentially the final frozen configuration. Finite-size effects are such that in the absorbing phase the final configuration is reached in a characteristic time that scales logarithmically with system size, while in the active phase, finite-size fluctuations take the system to a frozen configuration in a characteristic time that grows exponentially with system size. There is also a class of finite-size topological transition associated with group splitting in the network of these final frozen configurations.

Stability and bifurcation in a stochastic vocal folds model

In this paper, the stability and bifurcation in a class of stochastic vocal folds dynamical model are investigated. We use polar coordinate, Taylor expansion and stochastic averaging method to transform our classic system into an Itô averaging diffusion system. Also, we recall some theorems that give us some conditions which leads to sufficient conditions on drift and diffusion coefficients for stochastic stability and P-bifurcation of the model. Finally, numerical simulations are presented to show the effects of the noise intensity and illustrate our theoretical results.

Probabilistic Energy Management for Building Climate Comfort in Smart Thermal Grids with Seasonal Storage Systems

This paper presents an energy management framework for building climate comfort (BCC) systems interconnected in a grid via aquifer thermal energy storage (ATES) systems in the presence of two types of uncertainty (private and common). ATES can be used either as a heat source (hot well) or sink (cold well) depending on the season. We consider the uncertain thermal energy demand of individual buildings as a private uncertainty source and the uncertain common resource pool (ATES) between neighbors as a common uncertainty source. We develop a large-scale stochastic hybrid dynamical model to predict the thermal energy imbalance in a network of interconnected BCC systems together with mutual interactions between their local ATES. We formulate a finite-horizon mixed-integer quadratic optimization problem with multiple chance constraints at each sampling time, which is in general a non-convex problem and difficult to solve. We then provide a computationally tractable framework by extending the so-called robust randomized approach and offering a less conservative solution for a problem with multiple chance constraints. A simulation study is provided to compare completely decoupled, centralized and move-blocking centralized solutions. We also present a numerical study using a geohydrological simulation environment (MODFLOW) to illustrate the advantages of our proposed framework.

Stoneley wave attenuation and dispersion and the dynamic permeability correction

Stoneley waves induce fluid pressure gradients in a permeable formation surrounding the borehole. These gradients are equilibrated through pressure diffusion, that is to say, slow P-waves in the context of Biot’s poroelasticity theory. Because slow P-waves are strongly sensitive to the formation permeability, the Stoneley-slow P-wave interaction can be used to retrieve the formation permeability from the attenuation and dispersion of Stoneley waves. The accuracy of this established technique in high-permeability formations deteriorates when slow P-waves are not pure diffusion waves; hence, the permeability dependence is more complicated. This effect on Stoneley waves is captured by applying the Johnson-Koplik-Dashen dynamic permeability model. Their model depends on a viscous relaxation length. However, in the estimation of formation permeability from Stoneley waves, this parameter is typically not measured but is estimated from an empirical equation, wherein material properties and microstructural descriptors are lumped together. When the so-calculated relaxation length is erroneous, the inverted formation permeability from the Stoneley wave is not correct either. To overcome this limitation and to provide a versatile alternative, the dynamic permeability problem is reformulated within the viscosity-extended Biot framework. Its physical basis is the conversion scattering in random media from slow P- to slow S-waves. The correlation length of this so-called stochastic dynamic permeability model can be derived from pore-scale images, and it also captures the effect of pore interface roughness. This model is then combined with the simplified Biot-Rosenbaum model to predict Stoneley wave attenuation and dispersion. We have applied this hybrid model to interpret laboratory measurements for which the previously suggested choice of the viscous relaxation length does not provide an accurate prediction. The results indicate that the hybrid model can provide another approach to model Stoneley wave attenuation and dispersion across the entire frequency range.

Investigation of Gear Dynamic Characteristics under Stochastic External Excitations

Engine drive gear systems are widely used in lots of mechanical equipment. In engine drive gear systems, the external excitations, including the driving speed and external load, are generally stochastic due to manufacturing error, energy loss, variation of operating environmental, and so on. The reported works usually considered them as deterministic. In this paper, a stochastic nonlinear gear dynamic model considering the stochastic external excitations is presented. Then, the effects of the stochastic driving speed and external load on gear dynamic characteristics are investigated by Monte Carlo (MC) simulation. By the simulation results, some insightful conclusions, which are important for the gear random dynamics, are obtained.

Nonparametric Identification in the Dynamic Stochastic Block Model

We show nonparametric identification of the parameters in the dynamic stochastic block model as recently introduced by Matias and Miele (2017) in the case of binary, finitely weighted, and general edge states. We formulate conditions on the true parameters, which guarantee actual point identification instead of mere generic identification, and which also lead to novel conclusions in the static case. In particular, our results justify in terms of the identification of the applications by Matias and Miele to finitely weighted edges with three edge states. We also give numerical illustrations via the variational EM algorithm in simulation settings covered by our identification analysis.

Deadbands, Droop, and Inertia Impact on Power System Frequency Distribution

Power system inertia is falling as more energy is supplied by renewable generators, and there are concerns about the frequency controls required to guarantee satisfactory system performance. The majority of research into the negative effect of low inertia has focused on poor dynamic response following major disturbances, when the transient frequency dip can become unacceptable. However, another important practical concern—keeping average frequency deviations within acceptable limits—was mainly out of the sight of the research community. In this manuscript, we present a method for finding the frequency probability density function (PDF) for a given power system. We pass from an initial stochastic dynamic model to deterministic equations for the frequency PDF, which are analyzed to uncover key system parameters influencing frequency deviations. We show that system inertia has little effect on the frequency PDF, making virtual inertia services insufficient for keeping frequency close to nominal under ambient load fluctuations. We establish that aggregate system droop and deadband width are the only parameters that have major influence on the average frequency deviations, suggesting that energy storage might be an excellent solution for tight frequency regulation. We also show that changing the governor deadband width does not significantly affect generator movement.

A Keynesian Dynamic Stochastic Disequilibrium model for business cycle analysis

A Dynamic Stochastic Disequilibrium model is proposed for business cycle analysis. The core innovation and fundamental deviation from the corresponding full-employment Dynamic Stochastic General Equilibrium model is the assumption that the nominal wage is a policy variable with no tendency to clear the labor market. As a consequence, disequilibrium unemployment arises which crucially alters the transmission of macroeconomic shocks. Solving the puzzle of low fiscal multipliers in conventional general equilibrium models, the effects of spending shocks become considerably more pronounced in the disequilibrium model because idle labor can be quickly utilized to accommodate aggregate demand without requiring households to increase their supply. In contrast to the standard model, technology and labor supply shocks are partly absorbed by unemployment and, hence, only moderately expansionary. Despite its simplicity and unlike the corresponding general equilibrium model, the disequilibrium model is able to generate shock responses which are broadly in line with empirical evidence.

Modeling optimal responses and fitness consequences in a changing Arctic.

Animals must balance a series of costs and benefits while trying to maximize their fitness. For example, an individual may need to choose how much energy to allocate to reproduction versus growth, or how much time to spend on vigilance versus foraging. Their decisions depend on complex interactions between environmental conditions, behavioral plasticity, reproductive biology, and energetic demands. As animals respond to novel environmental conditions caused by climate change, the optimal decisions may shift. Stochastic dynamic programming provides a flexible modeling framework with which to explore these trade-offs, but this method has not yet been used to study possible changes in optimal trade-offs caused by climate change. We created a stochastic dynamic programming model capturing trade-off decisions required by an individual adult female polar bear (Ursus maritimus) as well as the fitness consequences of her decisions. We predicted optimal foraging decisions throughout her lifetime as well as the energetic thresholds below which it is optimal for her to abandon a reproductive attempt. To explore the effects of climate change, we shortened the spring feeding period by up to 3weeks, which led to predictions of riskier foraging behavior and higher reproductive thresholds. The resulting changes in fitness may be interpreted as a best-case scenario, where bears adapt instantaneously and optimally to new environmental conditions. If the spring feeding period was reduced by 1week, her expected fitness declined by 15%, and if reduced by 3weeks, expected fitness declined by 68%. This demonstrates an effective way to explore a species' optimal response to a changing landscape of costs and benefits and highlights the fact that small annual effects can result in large cumulative changes in expected lifetime fitness.

Displacement Reliability Analysis of Submerged Multi-body Structure’s Floating Body for Connection Gaps

Abstract Aiming at the problem of systems’ dynamic characteristics’ randomness caused by connection gaps of submerged multi-body structures, a stochastic and uncertainty dynamical model were formulated for connection gaps and dynamic elongation of mooring cables. This model considered sag effect caused by light, soft and low damping characteristics of mooring cables and their dynamic elongation under the impact of flow field and connection gaps. The equivalent elastic modulus method was used to modify the sag effect. The Newmark-β method was used to solve the problem. Calculation results showed that the average value and peak value of floating body displacement caused by uncertainty of gap contact states are larger than those of ideal articulated states. The reliability of floating body’s displacement with gap contact will be reduced to different extents and the reliability of displacement in velocity direction changes greatly, especially perpendicular to flow field. When studying multi-body structures, randomness of contact state should be considered to reduce the dispersion of clearance and improve dynamic performance.

A Reliable Numerical Analysis for Stochastic Hepatitis B Virus Epidemic Model with the Migration Effect

The dynamics of an infectious disease in a population has a stochastic nature. Considering this stochastic behavior is more desirable when modeling the epidemics. Analyzing a stochastic model gives more insight as compared to its deterministic part only. This work presents a reliable numerical analysis for stochastic hepatitis B virus epidemic model with the migration effect. The outcomes of stochastic hepatitis B model are compared with its corresponding deterministic part. The dynamics of stochastic model is dependent upon a parameter $$H^{*}$$ , called basic reproductive number. As the value of $$H^{*}$$ changes from greater than 1 to less than 1, the dynamics of disease switches from endemic to infection-free state. In this paper, a structure-preserving numerical method is proposed for the analysis of stochastic hepatitis B model. The results obtained using MATLAB programs are compared with existing schemes in the literature which have certain limitations regarding stability and dynamical consistency. The proposed scheme remains stable and consistent for all choices of parameter values.

Utilization Management and Pricing of Parking Facilities Under Uncertain Demand and User Decisions

Excessive search for parking spots in congested areas contributes to additional travel delays and negative socio-economic impacts. While managing parking utilization to address the agency’s objectives, it is often very beneficial to reflect the diversity of users’ behaviors and their travel choices. This paper develops a stochastic dynamic parking management model, under competitive user-agency perceptions and uncertain user demand and parking occupancy, to simultaneously minimize the total travelers’ costs and maximize the parking agency’s revenue. The problem is formulated into a dynamic programming model and solved using a stochastic look-ahead technique based on the Monte Carlo tree search algorithm to determine optimal actions on parking price assignment and spot utilization over time. The numerical experiments on a hypothetical and empirical case study are conducted to show the performance of the proposed algorithm and to draw managerial insights. The results are compared with those of benchmark algorithms, which indicate that the proposed methodology can determine near-optimal solutions efficiently.

The complex transmission seasonality of hand, foot, and mouth disease and its driving factors

BackgroundThe transmission rate seasonality is an important index for transmission dynamics in many childhood infections, and has been widely studied in industrialized countries. However, it has been neglected in the study of pathogens in China.MethodsTo understand the transmission dynamics of hand, foot and mouth disease (HFMD), we examined the transmission rate seasonality of HFMD in three provinces, Henan, Anhui and Chongqing, in China, using a dynamical stochastic SIR model. We investigated potential driving factors, including school terms, the Chinese Spring Festival period, meteorological factors and population flux for their effects on the HFMD transmission seasonality using multiple regression models.ResultsThe transmission rate of HFMD had complex seasonality with one large major peak in March and one small peak in autumn. School terms, the Chinese Spring Festival period, population flux and meteorological factors had combined effects on the HFMD transmission seasonality in mainland China. The school terms reflects the seasonal contact rate in Children, while the population flux and the Chinese Spring Festival period reflect the seasonal contact rate in population. They drove HFMD transmission rate seasonality in different time periods of the year in China. Contact rate seasonality in population dominated effects on HFMD transmission in February and March. The dramatic increase in transmission rate during February coincides with the Chinese Spring Festival period and high population flux in this month. The contact rate seasonality in children dominated effects on the transmission in the other months of the year in Chongqing. Meteorological factors can not solely explain the seasonality in HFMD transmission in mainland China; however, they may have combined effects with school terms and the highway passenger traffic on the transmission rate in Anhui during the fall semester.ConclusionThe transmission rate of HFMD in three provinces in China had complex seasonality. The Chinese Spring Festival period, population flux and (or) school terms explained the majority of the transmission rate seasonality of HFMD, and they drove HFMD transmission rate seasonality in different time periods of the year. The Chinese Spring Festival period dominantly caused the dramatic increase of the HFMD transmission rate during February.

Bridging the gap between individual-based and continuum models of growing cell populations.

Continuum models for the spatial dynamics of growing cell populations have been widely used to investigate the mechanisms underpinning tissue development and tumour invasion. These models consist of nonlinear partial differential equations that describe the evolution of cellular densities in response to pressure gradients generated by population growth. Little prior work has explored the relation between such continuum models and related single-cell-based models. We present here a simple stochastic individual-based model for the spatial dynamics of multicellular systems whereby cells undergo pressure-driven movement and pressure-dependent proliferation. We show that nonlinear partial differential equations commonly used to model the spatial dynamics of growing cell populations can be formally derived from the branching random walk that underlies our discrete model. Moreover, we carry out a systematic comparison between the individual-based model and its continuum counterparts, both in the case of one single cell population and in the case of multiple cell populations with different biophysical properties. The outcomes of our comparative study demonstrate that the results of computational simulations of the individual-based model faithfully mirror the qualitative and quantitative properties of the solutions to the corresponding nonlinear partial differential equations. Ultimately, these results illustrate how the simple rules governing the dynamics of single cells in our individual-based model can lead to the emergence of complex spatial patterns of population growth observed in continuum models.

Analytical computation method for steady-state stochastic response of a time-delay nonlinear automotive suspension system

Abstract A novel analytical computation method of steady-state probability density function (PDF) is presented to solve the stochastic response of a time-delay nonlinear automotive suspension system. In accordance with actual projects, a stochastic dynamics model of the automotive suspension system is established which includes cubic nonlinear restoring force, time-delay feedback control term and random road excitation simulated by white Gaussian noise. Based on the averaged angular frequency derived from Hamiltonian function of the nonlinear conservative system associated with the established stochastic dynamics model, the original system is transformed into a stochastic differential dynamics system without time-delay terms. By using generalized harmonic function-based stochastic averaging method and deterministic averaging method, the averaged Ito stochastic differential equation associated with the transformed system is obtained. Through solving the averaged Fokker-Planck-Kolmogorov equation established by drift and diffusion coefficients of the Ito equation, the steady-state PDFs of stochastic response amplitude and systematic energy as well as the steady-state joint PDF of stochastic response are obtained. All of the analytical results are verified by digital simulations.

Affordable Housing and City Welfare

Housing affordability is the main policy challenge for most large cities in the world. Zoning changes, rent control, housing vouchers, and tax credits are the main levers employed by policy makers. How effective are they at combatting the affordability crisis? We build a dynamic stochastic spatial equilibrium model to evaluate the effect of these policies on the well-being of its citizens. The model endogenizes house prices, rents, construction, labor supply, output, income and wealth inequality, the location decisions of households within the city as well as inter-city migration. Its main novel features are risk, risk aversion, and incomplete risk-sharing. We calibrate the model to the New York MSA. Housing affordability policies carry substantial insurance value but affect aggregate housing and labor supply and cause misallocation in labor and housing markets. Housing affordability policies that enhance access to this insurance especially for the neediest households create substantial net welfare gains.

Driver Surge Pricing

Ride-hailing marketplaces like Uber and Lyft use dynamic pricing, often called surge, to balance the supply of available drivers with the demand for rides. We study driver-side payment mechanisms for such marketplaces, presenting the theoretical foundation that has informed the design of Uber's new additive driver surge mechanism. We present a dynamic stochastic model to capture the impact of surge pricing on driver earnings and their strategies to maximize such earnings. In this setting, some time periods (surge) are more valuable than others (non-surge), and so trips of different time lengths vary in the induced driver opportunity cost. First, we show that multiplicative surge, historically the standard on ride-hailing platforms, is not incentive compatible in a dynamic setting. We then propose a structured, incentive-compatible pricing mechanism. This closed-form mechanism has a simple form and is well-approximated by Uber's new additive surge mechanism. Finally, through both numerical analysis and real data from a ride-hailing marketplace, we show that additive surge is more incentive compatible in practice than is multiplicative surge.

Continuous-Time Opinion Dynamics With Stochastic Multiplicative Noises

Recently, the study of opinion dynamics on complex networks has attracted a great deal of attention. In this brief, we take an interest in how an opinion forms in a social network with stochastic noises. We investigate a stochastic opinion dynamics model, in which individuals obtain information from their neighbors in a social network. We model the social network as a strongly connected graph. Each individual has an initial opinion and iteratively exchanges her opinion based on a stubborn opinion, her neighbors’ opinions and small stochastic noises continually. We first construct a general stochastic opinion evolution problem with multiplicative noises as a stochastic differential equation and then investigate the stochastic stability of this equation. We consider whether an opinion may form as a result of stochastic disturbance and local interactions. We also establish two sufficient conditions which ensure that the average opinion and the error vector system for all individuals are stochastic stable, respectively. Numerical simulations are given to demonstrate the effectiveness of the theoretical results.