Numerical solution of stochastic state-dependent delay differential equations: convergence and stability

被引：2
作者：
Akhtari, Bahar [1 ]
机构：
[1] IASBS, Dept Math, Zanjan, Iran
来源：
ADVANCES IN DIFFERENCE EQUATIONS | 2019年 / 2019卷 / 01期
关键词：
BACKWARD EULER METHOD; EXPONENTIAL STABILITY; SCHEMES; APPROXIMATION; EXISTENCE;
D O I：
10.1186/s13662-019-2323-x
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
Numerical analysis of stochastic delay differential equations has been widely developed but frequently for the cases where the delay term has a simple feature. In this paper, we aim to study a more general case of delay term which has not been much discussed so far. We mean the case where the delay term takes random values. For this purpose, a new continuous split-step scheme is introduced to approximate the solution and then convergence in the mean-square sense is investigated. Moreover, given a test equation, the mean-square asymptotic stability of the scheme is presented. Numerical examples are provided to further illustrate the obtained theoretical results.
引用
收藏
页数：34
相关论文
共 32 条
[1]   AN EULER SCHEME FOR STOCHASTIC DELAY DIFFERENTIAL EQUATIONS ON UNBOUNDED DOMAINS: PATHWISE CONVERGENCE [J].
Akhtari, Bahareh ;
Babolian, Esmail ;
Neuenkirch, Andreas .
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B, 2015, 20 (01) :23-38
[2]   Existence and controllability results for second-order impulsive stochastic evolution systems with state-dependent delay [J].
Arthi, G. ;
Park, Ju H. ;
Jung, H. Y. .
APPLIED MATHEMATICS AND COMPUTATION, 2014, 248 :328-341
[3]  
Baker C. T. H., 2000, LMS Journal of Computation and Mathematics, V3
[4]   Exponential stability in p-th mean of solutions, and of convergent Euler-type solutions, of stochastic delay differential equations [J].
Baker, CTH ;
Buckwar, E .
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2005, 184 (02) :404-427
[5]   Almost sure exponential stability of the backward Euler-Maruyama scheme for stochastic delay differential equations with monotone-type condition [J].
Chen, Lin ;
Wu, Fuke .
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2015, 282 :44-53
[6]   Existence and uniqueness of the solutions and convergence of semi-implicit Euler methods for stochastic pantograph equations [J].
Fan, Zhencheng ;
Liu, Mingzhu ;
Cao, Wanrong .
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2007, 325 (02) :1142-1159
[7]  
Guo Q., 2013, J INF COMPUT SCI, V10, P1261, DOI [10.12733/jics20101622, DOI 10.12733/JICS20101622]
[8]   A Note on Euler Approximations for Stochastic Differential Equations with Delay [J].
Gyoengy, Istvan ;
Sabanis, Sotirios .
APPLIED MATHEMATICS AND OPTIMIZATION, 2013, 68 (03) :391-412
[9]  
Higham D.J., 2003, LMS J. Comput. Math., V6, P297, DOI DOI 10.1112/S1461157000000462
[10]   Mean-square and asymptotic stability of the stochastic theta method [J].
Higham, DJ .
SIAM JOURNAL ON NUMERICAL ANALYSIS, 2000, 38 (03) :753-769
1234