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

Lin Chen

DOI: 10.4208/jcm.1808-m2018-0005

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

Published online: 2019-03

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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.

  • Keywords

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

  • AMS Subject Headings

60H10, 65C20, 65L20

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

cl18971072943@163.com (Lin Chen)

  • BibTex
  • RIS
  • TXT
@Article{JCM-37-704, author = {Chen , Lin}, title = {Stability of the Stochastic θ-Method for Super-Linear Stochastic Differential Equations with Unbounded Delay}, journal = {Journal of Computational Mathematics}, year = {2019}, volume = {37}, number = {5}, pages = {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.

}, issn = {1991-7139}, doi = {https://doi.org/10.4208/jcm.1808-m2018-0005}, url = {http://global-sci.org/intro/article_detail/jcm/13042.html} }
TY - JOUR T1 - Stability of the Stochastic θ-Method for Super-Linear Stochastic Differential Equations with Unbounded Delay AU - Chen , Lin JO - Journal of Computational Mathematics VL - 5 SP - 704 EP - 720 PY - 2019 DA - 2019/03 SN - 37 DO - http://doi.org/10.4208/jcm.1808-m2018-0005 UR - https://global-sci.org/intro/article_detail/jcm/13042.html KW - Unbounded delay, Monotone condition, Polynomial condition, Stochastic θ-method, Decay stability. AB -

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.

Chen , Lin. (2019). Stability of the Stochastic θ-Method for Super-Linear Stochastic Differential Equations with Unbounded Delay. Journal of Computational Mathematics. 37 (5). 704-720. doi:10.4208/jcm.1808-m2018-0005
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