STABILITY OF THE STOCHASTIC θ-METHOD FOR SUPER-LINEAR STOCHASTIC DIFFERENTIAL EQUATIONS WITH UNBOUNDED DELAY

• 来源期刊: 计算数学（英文版）
• 关键词: Unbounded delay Monotone condition Polynomial condition Stochastic θ-method Decay stability
• 年，卷（期）: 2019,（5）
• 页码范围: 704-720
• 页数: 17页
• 语种: 英文
• DOI: 10.4208/jcm.1808-m2018-0005

摘要

This paper deals with numerical stability properties of super-linear stochastic differential equations with unbounded delay.Sufficient conditions for mean square and almost sure decay stability of the above system and its stochastic θ-method approximation are investigated in this paper.The author establishes numerical stability under a monotone-type condition in unbounded delay setting.An example is presented to illustrate the result.