Stability of the Stochastic θ-Method for Super-Linear Stochastic Differential Equations with Unbounded Delay

Stability of the Stochastic θ-Method for Super-Linear Stochastic Differential Equations with Unbounded Delay

Year:    2019

Author:    Lin Chen

Journal of Computational Mathematics, Vol. 37 (2019), Iss. 5 : pp. 704–720

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.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/jcm.1808-m2018-0005

Journal of Computational Mathematics, Vol. 37 (2019), Iss. 5 : pp. 704–720

Published online:    2019-01

AMS Subject Headings:   

Copyright:    COPYRIGHT: © Global Science Press

Pages:    17

Keywords:    Unbounded delay Monotone condition Polynomial condition Stochastic θ-method Decay stability.

Author Details

Lin Chen