A stochastic two-dimensional intelligent driver car-following model with vehicular dynamics

The law of vehicle movement has long been studied under the umbrella of microscopic traffic flow models,especially the car-following(CF)models.These models of the movement of vehicles serve as the backbone of traffic flow analysis,simulation,autonomous vehicle development,etc.Two-dimensional(2D)vehicular movement is basically stochastic and is the result of interactions between a driver's behavior and a vehicle's characteristics.Current microscopic models either neglect 2D noise,or overlook vehicle dynamics.The modeling capabilities,thus,are limited,so that stochastic lateral movement cannot be reproduced.The present research extends an intelligent driver model(IDM)by explicitly considering both vehicle dynamics and 2D noises to formulate a stochastic 2D IDM model,with vehicle dynamics based on the stochastic differential equation(SDE)theory.Control inputs from the vehicle include the steer rate and longitudinal acceleration,both of which are developed based on an idea from a traditional intelligent driver model.The stochastic stability condition is analyzed on the basis of Lyapunov theory.Numerical analysis is used to assess the two cases:(i)when a vehicle accelerates from a standstill and(ii)when a platoon of vehicles follow a leader with a stop-and-go speed profile,the formation of congestion and subsequent dispersion are simulated.The results show that the model can reproduce the stochastic 2D trajectories of the vehicle and the marginal distribution of lateral movement.The proposed model can be used in both a simulation platform and a behavioral analysis of a human driver in traffic flow.

Dynamic corner frequency in source spectral model for stochastic synthesis of ground motion

The static comer frequency and dynamic comer frequency in stochastic synthesis of ground motion from fi- nite-fault modeling are introduced, and conceptual disadvantages of the two are discussed in this paper. Furthermore, the non-uniform radiation of seismic wave on the fault plane, as well as the trend of the larger rupture area, the lower comer frequency, can be described by the source spectral model developed by the authors. A new dynamic comer frequency can be developed directly from the model. The dependence of ground motion on the size of subfault can be eliminated if this source spectral model is adopted in the synthesis. Finally, the approach presented is validated from the comparison between the synthesized and observed ground motions at six rock stations during the Northridge earthquake in 1994.

Exit problem of stochastic SIR model with limited medical resource

Nonlinearity and randomness are both the essential attributes for the real world,and the case is the same for the models of infectious diseases,for which the deterministic models can not give a complete picture of the evolution.However,although there has been a lot of work on stochastic epidemic models,most of them focus mainly on qualitative properties,which makes us somewhat ignore the original meaning of the parameter value.In this paper we extend the classic susceptible-infectious-removed(SIR)epidemic model by adding a white noise excitation and then we utilize the large deviation theory to quantitatively study the long-term coexistence exit problem with epidemic.Finally,in order to extend the meaning of parameters in the corresponding deterministic system,we tentatively introduce two new thresholds which then prove rational.

Stochastic Dynamic Modeling of Rain Attenuation: A Survey

Satellite communication systems(SCS) operating on frequency bands above 10 GHz are sensitive to atmosphere physical phenomena, especially rain attenuation. To evaluate impairments in satellite performance, stochastic dynamic modeling(SDM) is considered as an effective way to predict real-time satellite channel fading caused by rain. This article carries out a survey of SDM using stochastic differential equations(SDEs) currently in the literature. Special attention is given to the different input characteristics of each model to satisfy specific local conditions. Future research directions in SDM are also suggested in this paper.

THE TURNPIKE IN DYNAMIC STOCHASTIC ECONOMIC GROWTH MODELS FOR STATE－CONTINGENT CAPITAL STOCKS

A stochastic economic growth model may be transformed into a deterministic economic growth model with an infiaite dimentional Banach space of state-contingent capital stocks [6]. This paper proves that under the framework, the stochastic analogUes of the asymptotic turnpike theorems in the standard deterministic economic growth model [5] will continue tO hold if we assume that essentially smooth programs satisfy uniformly essentially dominant diagonal condition.

A Three-Stage Stochastic Dynamic Pricing Game Model Affected by New Products into the Market

In real-life marketing, a common phenomenon is that the prices of current product will have been cut down even the new product has not gone into market yet. Thus, it is very important for merchant to set the strategy which can make the excepted revenue maximum. So, this paper constructs a three-stage stochastic dynamic pricing game model for analyzing the influence of the uncertainty of entry timing of the new products on pricing of products being sold. By analyzing of the pricing strategy, there are big differences in the predictions of new product going into market between merchant and customers;the merchant will adopt cutting price for promotion strategy to reduce negative influence of the new products on the demand of the products sold now. Otherwise, the merchant will adopt the strategy of maximizing current period’s profit.

Stochastic dynamic simulation of railway vehicles collision using data-driven modelling approach

Using stochastic dynamic simulation for railway vehicle collision still faces many challenges,such as high modelling complexity and time-consuming.To address the challenges,we introduce a novel data-driven stochastic process modelling(DSPM)approach into dynamic simulation of the railway vehicle collision.This DSPM approach consists of two steps:(i)process description,four kinds of kernels are used to describe the uncertainty inherent in collision processes;(ii)solving,stochastic variational inferences and mini-batch algorithms can then be used to accelerate computations of stochastic processes.By applying DSPM,Gaussian process regression(GPR)and finite element(FE)methods to two collision scenarios(i.e.lead car colliding with a rigid wall,and the lead car colliding with another lead car),we are able to achieve a comprehensive analysis.The comparison between the DSPM approach and the FE method revealed that the DSPM approach is capable of calculating the corresponding confidence interval,simultaneously improving the overall computational efficiency.Comparing the DSPM approach with the GPR method indicates that the DSPM approach has the ability to accurately describe the dynamic response under unknown conditions.Overall,this research demonstrates the feasibility and usability of the proposed DSPM approach for stochastic dynamics simulation of the railway vehicle collision.

Dynamic Hedging Based on Markov Regime-Switching Dynamic Correlation Multivariate Stochastic Volatility Model

It is important to consider the changing states in hedging.The Markov regime-switching dynamic correlation multivariate stochastic volatility( MRS-DC-MSV) model was proposed to solve this issue. DC-MSV model and MRS-DC-MSV model were used to calculate the time-varying hedging ratios and compare the hedging performance. The Markov chain Monte Carlo( MCMC) method was used to estimate the parameters. The results showed that,there were obviously two economic states in Chinese financial market. Two models all did well in hedging,but the performance of MRS-DCMSV model was better. It could reduce risk by nearly 90%. Thus,in the hedging period,changing states is a factor that cannot be neglected.

StochSD: A Full Potential CSS Language for Dynamic and Stochastic Modelling, Simulation and Statistical Analysis

It is vital that a well-defined conceptual model can be realized by a macro-model (e.g., a Continuous System Simulation (CSS) model) or a micro-model (e.g., an Agent-Based model or Discrete Event Simulation model) and still produce mutually consistent results. The Full Potential CSS concept provides the rules so that the results from macro-modelling become fully consistent with those from micro-modelling. This paper focuses on the simulation language StochSD (Stochastic System Dynamics), which is an extension of classical Continuous System Simulation that implements the Full Potential CSS concept. Thus, in addition to modelling and simulating continuous flows between compartments represented by “real” numbers, it can also handle transitions of discrete entities by integer numbers, enabling combined models to be constructed in a straight-forward way. However, transition events of discrete entities (e.g., arrivals, accidents, deaths) usually happen irregularly over time, so stochasticity often plays a crucial role in their modelling. Therefore, StochSD contains powerful random functions to model uncertainties of different kinds, together with devices to collect statistics during a simulation or from multiple replications of the same stochastic model. Also, tools for sensitivity analysis, optimisation and statistical analysis are included. In particular, StochSD includes features for stochastic modelling, post-analysis of multiple simulations, and presentation of the results in statistical form. In addition to making StochSD a Full Potential CSS language, a second purpose is to provide an open-source package intended for small and middle-sized models in education, self-studies and research. To make StochSD and its philosophy easy to comprehend and use, it is based on the System Dynamics approach, where a system is described in terms of stocks and flows. StochSD is available for Windows, macOS and Linux. On the StochSD homepage, there is extensive material for a course in Modelling and Simulation in form of PowerPoint lectures and laboratory exercises.

Langevin approach with rescaled noise for stochastic channel dynamics in Hodgkin–Huxley neurons

The Langevin approach has been applied to model the random open and closing dynamics of ion channels. It has long been known that the gate-based Langevin approach is not sufficiently accurate to reproduce the statistics of stochastic channel dynamics in Hodgkin–Huxley neurons. Here, we introduce a modified gate-based Langevin approach with rescaled noise strength to simulate stochastic channel dynamics. The rescaled independent gate and identical gate Langevin approaches improve the statistical results for the mean membrane voltage, inter-spike interval, and spike amplitude.

Parametric Linear Stochastic Modelling of Benue River flow Process

The dynamics and accurate forecasting of streamflow processes of a river are important in the management of extreme events such as floods and droughts, optimal design of water storage structures and drainage networks. In this study, attempt was made at investigating the appropriateness of stochastic modelling of the streamflow process of the Benue River using data-driven models based on univariate streamflow series. To this end, multiplicative seasonal Autoregressive Integrated Moving Average (ARIMA) model was developed for the logarithmic transformed monthly flows. The seasonal ARIMA model’s performance was compared with the traditional Thomas-Fiering model forecasts, and results obtained show that the multiplicative seasonal ARIMA model was able to forecast flow logarithms. However, it could not adequately account for the seasonal variability in the monthly standard deviations. The forecast flow logarithms therefore cannot readily be transformed into natural flows;hence, the need for cautious optimism in its adoption, though it could be used as a basis for the development of an Integrated Riverflow Forecasting System (IRFS). Since forecasting could be a highly “noisy” application because of the complex river flow system, a distributed hydrological model is recommended for real-time forecasting of the river flow regime especially for purposes of sustainable water resources management.

Deterministic and Stochastic Fractional-Order Hastings-Powell Food Chain Model

In this paper,a deterministic and stochastic fractional-order model of the tri-trophic food chain model incorporating harvesting is proposed and analysed.The interaction between prey,middle predator and top predator population is investigated.In order to clarify the characteristics of the proposed model,the analysis of existence,uniqueness,non-negativity and boundedness of the solutions of the proposed model are examined.Some sufficient conditions that ensure the local and global stability of equilibrium points are obtained.By using stability analysis of the fractional-order system,it is proved that if the basic reproduction number R_(0)<1,the predator free equilibrium point E_(1) is globally asymptotically stable.The occurrence of local bifurcation near the equilibrium points is investigated with the help of Sotomayor’s theorem.Some numerical examples are given to illustrate the theoretical findings.The impact of harvesting on prey and themiddle predator is studied.We conclude that harvesting parameters can control the dynamics of the middle predator.A numerical approximation method is developed for the proposed stochastic fractional-order model.

Short and Long-Term Time Series Forecasting Stochastic Analysis for Slow Dynamic Processes

This paper intends to develop suitable methods to provide likely scenarios in order to support decision making for slow dynamic processes such as the underlying of agribusiness. A new method to analyze the short- and long-term time series forecast and to model the behavior of the underlying process using nonlinear artificial neural networks (ANN) is presented. The algorithm can effectively forecast the time-series data by stochastic analysis (Monte Carlo) of its future behavior using fractional Gaussian noise (fGn). The algorithm was used to forecast country risk time series for several countries, both for short term that is 30 days ahead and long term 350 days ahead scenarios.

Dynamical Modeling of the Nuclear Fission Process at Low Excitation Energies

Two recipes for modeling the dynamics of the nuclear fission process are known in literature. The underlying equations contain the driving, dissipative, and random forces. The two recipes are mostly different in the prescriptions for the driving force. In this work we carefully compare these driving forces and the resulting fission rates. It turns out that the rates may be very close or strongly different depending on the value the shell correction to the nuclear deformation energy. We give arguments in favor of one of the recipes.

Relationship between Maximum Principle and Dynamic Programming in Stochastic Differential Games and Applications

This paper is concerned with the relationship between maximum principle and dynamic programming in zero-sum stochastic differential games. Under the assumption that the value function is enough smooth, relations among the adjoint processes, the generalized Hamiltonian function and the value function are given. A portfolio optimization problem under model uncertainty in the financial market is discussed to show the applications of our result.

Modelling Bacterial Dynamics in Food Products: Role of Environmental Noise and Interspecific Competition

In this paper we review some results obtained within the context of the predictive microbiology, which is a specific field of the population dynamics. In particular we discuss three models, which exploit tools of statistical mechanics, for bacterial dynamics in food of animal origin. In the first model, the random fluctuating behaviour, experimentally measured, of the temperature is considered. In the second model stochastic differential equations are introduced to take into account the influence of physical and chemical variables, such as temperature, pH and activity water, subject to deterministic and random variations. The third model, which is an extended version of the second one, neglects the environmental fluctuations, and concentrates on the role of the interspecific bacterial interactions. The comparison between expected results and observed data indicates that the presence of noise sources and interspecific bacterial interactions improves the predictive features of the models analyzed.

A Comparison of Deterministic and Stochastic Susceptible-Infected-Susceptible (SIS) and Susceptible-Infected-Recovered (SIR) Models

In this paper we build and analyze two stochastic epidemic models with death. The model assumes that only susceptible individuals (S) can get infected (I) and may die from this disease or a recovered individual becomes susceptible again (SIS model) or completely immune (SIR Model) for the remainder of the study period. Moreover, it is assumed there are no births, deaths, immigration or emigration during the study period;the community is said to be closed. In these infection disease models, there are two central questions: first it is the disease extinction or not and the second studies the time elapsed for such extinction, this paper will deal with this second question because the first answer corresponds to the basic reproduction number defined in the bibliography. More concretely, we study the mean-extinction of the diseases and the technique used here first builds the backward Kolmogorov differential equation and then solves it numerically using finite element method with FreeFem++. Our contribution and novelty are the following: however the reproduction number effectively concludes the extinction or not of the disease, it does not help to know its extinction times because example with the same reproduction numbers has very different time. Moreover, the SIS model is slower, a result that is not surprising, but this difference seems to increase in the stochastic models with respect to the deterministic ones, it is reasonable to assume some uncertainly.

数字经济发展协同推进增长降碳的动态效应研究

构建居民、厂商(包含数字经济厂商)、政府3部门DSGE模型,重点研究数字基础设施、数字产业化、产业数字化等随机冲击协同推进增长降碳的动态效应及其传导机制。研究发现:数字基础设施、数字产业化、产业数字化3类数字经济随机技术冲击能够有效促进经济增长并减缓碳排放总量和碳排放强度;数字经济投资冲击能够显著减缓碳排放总量和碳排放强度,对数字经济产出和经济增长也有正向促进作用;数字经济对新型基础设施投资推动效应越强,所引致的环境经济效果越佳;数字经济结构调整能够显著推进数字经济产出和碳减排。整体来看,数字经济随机技术冲击、数字经济投资冲击、数字经济结构调整等不同政策呈现出增长降碳协同效应。