Strong convergence rate of the stochastic theta method for nonlinear hybrid stochastic differential equations with piecewise continuous arguments

被引：0
作者：
Yuhang Zhang
Minghui Song
Mingzhu Liu
Bowen Zhao
机构：
[1] Harbin Institute of Technology,School of Mathematics
来源：
Computational and Applied Mathematics | 2022年 / 41卷
关键词：
Stochastic differential equations with piecewise continuous arguments (SDEPCAs); Stochastic theta (ST) method; Forward–backward Euler–Maruyama (FBEM) method; Convergence rate; 65C30; 60H35;
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摘要：
We consider the strong convergence of the stochastic theta (ST) method for highly nonlinear hybrid stochastic differential equations with piecewise continuous arguments (SDEPCAs). There are three major ingredients. The first is the pth moment boundedness of the ST method. Second, the mean square convergence rate of the ST method for hybrid SDEPCAs is given by means of the forward–backward Euler–Maruyama method. The third ingredient is a numerical simulation, which shows the agreement with the theoretical convergence rate.
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[1]  
Hu J(2020)Advances in stabilization of hybrid stochastic differential equations by delay feedback control SIAM J Control Optim 58 735-754
[2]  
Liu W(2006)Option pricing with Markov-modulated dynamics SIAM J Control Optim 44 2063-2078
[3]  
Deng F(2014)Existence and exponential stability of solutions for stochastic cellular neural networks with piecewise constant argument J Appl Math 2014 451-463
[4]  
Mao X(2007)Convergence of numerical solution to stochastic delay differential equation with Poisson jump and Markovian switching Appl Math Comput 184 1080-1091
[5]  
Jobert A(2006)Convergence and stability of numerical solutions to SDDEs with Markovian switching Appl Math Comput 175 1435-1455
[6]  
Rogers LCG(2020)Stabilisation of highly nonlinear hybrid stochastic differential delay equations by delay feedback control Automatica 112 144-171
[7]  
Li X(2018)The numerical invariant measure of stochastic differential equations with Markovian switching SIAM J Numer Anal 56 936-948
[8]  
Li R(2013)Strong convergence rates for backward Euler–Maruyama method for non-linear dissipative-type stochastic differential equations with super-linear diffusion coefficients Stochastics 85 88-95
[9]  
Chang Z(2007)Approximations of Euler–Maruyama type for stochastic differential equations with Markovian switching, under non-lipschitz conditions J Comput Appl Math 205 280-293
[10]  
Li R(2014)Stabilization of hybrid stochastic differential equations by feedback control based on discrete-time state observations Syst Control Lett 73 2450-2477
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