scholarly journals The stochastic θ method for stationary distribution of stochastic differential equations with Markovian switching

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Yanan Jiang ◽  
Liangjian Hu ◽  
Jianqiu Lu
Keyword(s):  
Differential Equations ◽  
Numerical Simulations ◽  
Stochastic Differential Equations ◽  
Stationary Distribution ◽  
Existence And Uniqueness ◽  
Numerical Solutions ◽  
Markovian Switching ◽  
Theoretical Results

AbstractIn this paper, stationary distribution of stochastic differential equations (SDEs) with Markovian switching is approximated by numerical solutions generated by the stochastic θ method. We prove the existence and uniqueness of stationary distribution of the numerical solutions firstly. Then, the convergence of numerical stationary distribution to the underlying one is discussed. Numerical simulations are conducted to support the theoretical results.

scholarly journals Dynamics Analysis of a Stochastic Delay Gilpin-Ayala Model with Markovian Switching

2019 ◽  
Vol 2019 ◽  
pp. 1-15
Author(s):  
Qiaoqin Gao ◽  
Zhijiang Luo ◽  
Guirong Liu
Keyword(s):  
Numerical Simulations ◽  
Existence And Uniqueness ◽  
Matrix Method ◽  
Lyapunov Method ◽  
Markovian Switching ◽  
Dynamics Analysis ◽  
Stochastic Permanence ◽  
Stochastic Delay ◽  
Global Positive Solution ◽  
Theoretical Results

This paper considers a stochastic delay Gilpin-Ayala model with Markovian switching. Using Lyapunov method, we show existence and uniqueness of global positive solution. Then, by using Chebyshev’s inequality, M-matrix method, and BDG’s inequality, stochastic permanence and asymptotic estimations of solutions are studied. Finally, numerical simulations illustrate the theoretical results. Our results generalize and improve the existing results.

scholarly journals Stochastic Differential Equations with Multi-Markovian Switching

2013 ◽  
Vol 2013 ◽  
pp. 1-11
Author(s):  
Meng Liu ◽  
Ke Wang
Keyword(s):  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Classical Theory ◽  
Existence And Uniqueness ◽  
Markovian Switching ◽  
Uniqueness Of Solution

This paper is concerned with stochastic differential equations (SDEs) with multi-Markovian switching. The existence and uniqueness of solution are investigated, and thepth moment of the solution is estimated. The classical theory of SDEs with single Markovian switching is extended.

scholarly journals Stationary in Distributions of Numerical Solutions for Stochastic Partial Differential Equations with Markovian Switching

2013 ◽  
Vol 2013 ◽  
pp. 1-12 ◽  
Author(s):  
Yi Shen ◽  
Yan Li
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Stochastic Partial Differential Equations ◽  
Existence And Uniqueness ◽  
Numerical Solutions ◽  
Mild Solutions ◽  
Sufficient Conditions ◽  
Markovian Switching ◽  
Partial Differential ◽  
Stationary Distributions

We investigate a class of stochastic partial differential equations with Markovian switching. By using the Euler-Maruyama scheme both in time and in space of mild solutions, we derive sufficient conditions for the existence and uniqueness of the stationary distributions of numerical solutions. Finally, one example is given to illustrate the theory.

scholarly journals Modulo Periodic Poisson Stable Solutions of Quasilinear Differential Equations

Entropy ◽  
2021 ◽  
Vol 23 (11) ◽  
pp. 1535
Author(s):  
Marat Akhmet ◽  
Madina Tleubergenova ◽  
Akylbek Zhamanshin
Keyword(s):  
Differential Equations ◽  
Numerical Simulations ◽  
Existence And Uniqueness ◽  
Asymptotically Stable ◽  
Stable Solutions ◽  
Theoretical Results

In this paper, modulo periodic Poisson stable functions have been newly introduced. Quasilinear differential equations with modulo periodic Poisson stable coefficients are under investigation. The existence and uniqueness of asymptotically stable modulo periodic Poisson stable solutions have been proved. Numerical simulations, which illustrate the theoretical results are provided.

scholarly journals Existence and Uniqueness of Solution of Stochastic Dynamic Systems with Markov Switching and Concentration Points

2017 ◽  
Vol 2017 ◽  
pp. 1-5 ◽  
Author(s):  
Taras Lukashiv ◽  
Igor Malyk
Keyword(s):  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Dynamic Systems ◽  
Existence And Uniqueness ◽  
Markov Switching ◽  
Uniqueness Of Solution ◽  
Stochastic Dynamic ◽  
Uniqueness Of Solutions ◽  
Stochastic Dynamic Systems ◽  
Theoretical Results

In this article the problem of existence and uniqueness of solutions of stochastic differential equations with jumps and concentration points are solved. The theoretical results are illustrated by one example.

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