Comparing stochastic systems using regenerative simulation with common random numbers

1979 ◽  
Vol 11 (04) ◽  
pp. 804-819 ◽  
Author(s):  
Philip Heidelberger ◽  
Donald L. Iglehart
Keyword(s):  
Stochastic Models ◽  
Stochastic System ◽  
Variance Reduction ◽  
Stochastic Systems ◽  
Sufficient Conditions ◽  
Random Numbers ◽  
Numerical Examples ◽  
Common Random Numbers ◽  
Regenerative Simulation ◽  
Alternative Designs

Suppose two alternative designs for a stochastic system are to be compared. These two systems can be simulated independently or dependently. This paper presents a method for comparing two regenerative stochastic processes in a dependent fashion using common random numbers. A set of sufficient conditions is given that guarantees that the dependent simulations will produce a variance reduction over independent simulations. Numerical examples for a variety of simple stochastic models are included which illustrate the variance reduction achieved.

Comparing stochastic systems using regenerative simulation with common random numbers

1979 ◽  
Vol 11 (4) ◽  
pp. 804-819 ◽  
Author(s):  
Philip Heidelberger ◽  
Donald L. Iglehart
Keyword(s):  
Stochastic Models ◽  
Stochastic System ◽  
Variance Reduction ◽  
Stochastic Systems ◽  
Sufficient Conditions ◽  
Random Numbers ◽  
Numerical Examples ◽  
Common Random Numbers ◽  
Regenerative Simulation ◽  
Alternative Designs

Suppose two alternative designs for a stochastic system are to be compared. These two systems can be simulated independently or dependently. This paper presents a method for comparing two regenerative stochastic processes in a dependent fashion using common random numbers. A set of sufficient conditions is given that guarantees that the dependent simulations will produce a variance reduction over independent simulations. Numerical examples for a variety of simple stochastic models are included which illustrate the variance reduction achieved.

Dynamical behaviors of a prey-predator model with foraging arena scheme in polluted environments

2021 ◽  
Vol 71 (1) ◽  
pp. 235-250
Author(s):  
Xin He ◽  
Xin Zhao ◽  
Tao Feng ◽  
Zhipeng Qiu
Keyword(s):  
Periodic Solution ◽  
Stochastic System ◽  
Sufficient Conditions ◽  
Numerical Examples ◽  
Dynamical Behaviors ◽  
Analytical Results ◽  
Persistence In The Mean ◽  
The Mean ◽  
Predator Model

Abstract In this paper, a stochastic prey-predator model is investigated and analyzed, which possesses foraging arena scheme in polluted environments. Sufficient conditions are established for the extinction and persistence in the mean. These conditions provide a threshold that determines the persistence in the mean and extinction of species. Furthermore, it is also shown that the stochastic system has a periodic solution under appropriate conditions. Finally, several numerical examples are carried on to demonstrate the analytical results.

Results on Controllability of Nonlinear Hilfer Fractional Stochastic System

2019 ◽  
Vol 20 (3-4) ◽  
pp. 475-485 ◽  
Author(s):  
J. Priyadharsini ◽  
T. Sathiyaraj ◽  
P. Balasubramaniam
Keyword(s):  
Fractional Derivative ◽  
Stochastic System ◽  
Stochastic Systems ◽  
Dimensional Space ◽  
Sufficient Conditions ◽  
Finite Dimensional Space ◽  
Nonlinear Stochastic Systems ◽  
Hilfer Fractional Derivative ◽  
Finite Dimensional ◽  
Generalized Fractional Calculus

AbstractThe main objective of this paper is to present sufficient conditions for controllability of Hilfer fractional nonlinear stochastic systems in finite dimensional space. The main results are obtained by using the Nussbaum fixed point theorem, stochastic analysis approach and generalized fractional calculus (Hilfer fractional derivative) which is universality of Riemann-Liouville and Caputo fractional derivative. Finally, a numerical example is provided to show the effectiveness of the obtained theoretical result. The obtained result is more generalized one than the existing results on fractional stochastic system in finite dimensional space.

scholarly journals A Type of Time-Symmetric Stochastic System and Related Games

Symmetry ◽  
2021 ◽  
Vol 13 (1) ◽  
pp. 118
Author(s):  
Qingfeng Zhu ◽  
Yufeng Shi ◽  
Jiaqiang Wen ◽  
Hui Zhang
Keyword(s):  
Nash Equilibrium ◽  
Time Delay ◽  
Differential Equations ◽  
Equilibrium Point ◽  
Stochastic Differential Equations ◽  
Stochastic System ◽  
Stochastic Systems ◽  
Necessary Condition ◽  
Nash Equilibrium Point ◽  
Doubly Stochastic

This paper is concerned with a type of time-symmetric stochastic system, namely the so-called forward–backward doubly stochastic differential equations (FBDSDEs), in which the forward equations are delayed doubly stochastic differential equations (SDEs) and the backward equations are anticipated backward doubly SDEs. Under some monotonicity assumptions, the existence and uniqueness of measurable solutions to FBDSDEs are obtained. The future development of many processes depends on both their current state and historical state, and these processes can usually be represented by stochastic differential systems with time delay. Therefore, a class of nonzero sum differential game for doubly stochastic systems with time delay is studied in this paper. A necessary condition for the open-loop Nash equilibrium point of the Pontriagin-type maximum principle are established, and a sufficient condition for the Nash equilibrium point is obtained. Furthermore, the above results are applied to the study of nonzero sum differential games for linear quadratic backward doubly stochastic systems with delay. Based on the solution of FBDSDEs, an explicit expression of Nash equilibrium points for such game problems is established.

scholarly journals Finite-TimeH∞Control for Time-Delayed Stochastic Systems with Markovian Switching

2014 ◽  
Vol 2014 ◽  
pp. 1-10 ◽  
Author(s):  
Wenhua Gao ◽  
Feiqi Deng ◽  
Ruiqiu Zhang ◽  
Wenhui Liu
Keyword(s):  
Finite Time ◽  
State Feedback ◽  
Stochastic Systems ◽  
Sufficient Conditions ◽  
Markovian Switching ◽  
Time Stability ◽  
Finite Time Stability ◽  
Weighting Matrix ◽  
Simulation Results ◽  
Dependent State

This paper studies the problem of finite-timeH∞control for time-delayed Itô stochastic systems with Markovian switching. By using the appropriate Lyapunov-Krasovskii functional and free-weighting matrix techniques, some sufficient conditions of finite-time stability for time-delayed stochastic systems with Markovian switching are proposed. Based on constructing new Lyapunov-Krasovskii functional, the mode-dependent state feedback controller for the finite-timeH∞control is obtained. Simulation results illustrate the effectiveness of the proposed method.

scholarly journals Fuzzy Stabilization for Nonlinear Discrete Ship Steering Stochastic Systems Subject to State Variance and Passivity Constraints

2014 ◽  
Vol 2014 ◽  
pp. 1-12 ◽  
Author(s):  
Wen-Jer Chang ◽  
Bo-Jyun Huang ◽  
Po-Hsun Chen
Keyword(s):  
Linear Matrix Inequality ◽  
Discrete Time ◽  
Stochastic Systems ◽  
Fuzzy Controller ◽  
Controller Design ◽  
Sufficient Conditions ◽  
Control Technique ◽  
Linear Matrix ◽  
Matrix Inequality ◽  
Ship Steering

For nonlinear discrete-time stochastic systems, a fuzzy controller design methodology is developed in this paper subject to state variance constraint and passivity constraint. According to fuzzy model based control technique, the nonlinear discrete-time stochastic systems considered in this paper are represented by the discrete-time Takagi-Sugeno fuzzy models with multiplicative noise. Employing Lyapunov stability theory, upper bound covariance control theory, and passivity theory, some sufficient conditions are derived to find parallel distributed compensation based fuzzy controllers. In order to solve these sufficient conditions, an iterative linear matrix inequality algorithm is applied based on the linear matrix inequality technique. Finally, the fuzzy stabilization problem for nonlinear discrete ship steering stochastic systems is investigated in the numerical example to illustrate the feasibility and validity of proposed fuzzy controller design method.

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