Volume 37, Issue 5
Stability of the Stochastic θ-Method for Super-Linear Stochastic Differential Equations with Unbounded Delay

Lin Chen

10.4208/jcm.1808-m2018-0005

J. Comp. Math., 37 (2019), pp. 704-720.

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  • Abstract

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.

  • History

Published online: 2019-03

  • AMS Subject Headings

60H10, 65C20, 65L20

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