Journal of Guangdong University of Technology ›› 2011, Vol. 28 ›› Issue (1): 50-53.

• Comprehensive Studies • Previous Articles     Next Articles

Mean-Square Stability Analysis of EulerMaruyama Method for Scalar Stochastic Delay Differential Equations

  

  1. Faculty of Applied Mathematics, Guangdong University of Technology, Guangzhou 510006, China
  • Online:2011-12-25 Published:2011-12-25

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Abstract: Mean-square stability of EulerMaruyama method is studied for scalar stochastic delay differential equations with multiplicative noise under the condition of analytical meansquare stability.It is proven that the numerical solution is meansquare stable when the stepsize satisfies certain restrictions.Numerical examples verify the theoretical results.

Key words: stochastic delay differential equations; Euler-Maruyama method; mean-square stability

［1］ Mao X R.Stochastic differential equations and applications［M］.Second Edition.Chichester: Harwood, 2007.147-234.

［2］ Zhou S B, Wang Z Y, Feng D.Stochastic functional differential equations with infinite delay［J］.J Math Anal Appl, 2009(357): 416-426.

［3］ Li C X, Sun J T, Sun R Y.Stability analysis of a class of stochastic differential delay equations with nonlinear impulsive effects［J］.Journal of the Franklin Institute, 2010(347): 1186-1198.

［4］ Cao W R, Liu M Z, Fan Z C.MSstability of the EulerMaruyama method for stochastic differential delay equations［J］.Appl Math Comput, 2004(159): 127-135.

［5］ Li R H, Meng H B, Dai Y H.Convergence of numerical solutions to stochastic delay differential equations with jumps［J］.Appl Math Comput, 2006(172): 584-602.

［6］ Liu M Z, Cao W R, Fan Z C.Convergence and stability of the semiimplicit Euler method for a linear stochastic differential delay equation［J］.J Comput Appl Math, 2004(170): 255-268.

［7］ Fan Z C, Liu M Z, Cao W R.Existence and uniqueness of the solutions and convergence of semiimplicit Euler methods for stochastic pantograph equations［J］.J Math Anal Appl, 2007(325): 1142-1159.

［8］ Zhang H M, Gan S Q, Hu L.The splitstep backward Euler method for linear stochastic delay differential equations［J］.J Comput Appl Math, 2009(225): 558-568.

［9］ 谭英贤, 甘四清.中立型随机比例延迟微分方程平衡半隐式Euler方法的均方收敛性［J］.数学理论与应用, 2009, 29(4): 47-51.

［10］ Zhao G H, Song M H, Liu M Z.Exponential stability of EulerMaruyama solutions for impulsive stochastic differential equations with delay［J］.Appl Math Comput, 2010(215): 3425-3432.

［11］ Mohammed S E A.Stochastic functional differential equations［M］.Boston: Pitman Advanced Publishing Program, 1984.

［12］ Mao X R.Exponential stability of stochastic differential equations［M］.New York: Marcel Dekker, 1994.147-290.

［13］ Maruyama G.Continuous Markov processes and stochastic equations［J］.Rend Circolo Math Palermo, 1955(4): 48-90.

［14］ 曹婉容.随机延迟微分方程几种数值方法的收敛性和稳定性［D］.哈尔滨:哈尔滨工业大学博士学位论文，2004.
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