Mean-Square Convergence of Drift-Implicit One-Step Methods for Neutral Stochastic Delay Differential Equations with Jump Diffusion
Joint Authors
Source
Discrete Dynamics in Nature and Society
Issue
Vol. 2011, Issue 2011 (31 Dec. 2011), pp.1-22, 22 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2011-11-30
Country of Publication
Egypt
No. of Pages
22
Main Subjects
Abstract EN
A class of drift-implicit one-step schemes are proposed for the neutral stochastic delay differential equations (NSDDEs) driven by Poisson processes.
A general framework for mean-square convergence of the methods is provided.
It is shown that under certain conditions global error estimates for a method can be inferred from estimates on its local error.
The applicability of the mean-square convergence theory is illustrated by the stochastic θ-methods and the balanced implicit methods.
It is derived from Theorem 3.1 that the order of the mean-square convergence of both of them for NSDDEs with jumps is 1/2.
Numerical experiments illustrate the theoretical results.
It is worth noting that the results of mean-square convergence of the stochastic θ-methods and the balanced implicit methods are also new.
American Psychological Association (APA)
Hu, Lin& Gan, Siqing. 2011. Mean-Square Convergence of Drift-Implicit One-Step Methods for Neutral Stochastic Delay Differential Equations with Jump Diffusion. Discrete Dynamics in Nature and Society،Vol. 2011, no. 2011, pp.1-22.
https://search.emarefa.net/detail/BIM-508005
Modern Language Association (MLA)
Hu, Lin& Gan, Siqing. Mean-Square Convergence of Drift-Implicit One-Step Methods for Neutral Stochastic Delay Differential Equations with Jump Diffusion. Discrete Dynamics in Nature and Society No. 2011 (2011), pp.1-22.
https://search.emarefa.net/detail/BIM-508005
American Medical Association (AMA)
Hu, Lin& Gan, Siqing. Mean-Square Convergence of Drift-Implicit One-Step Methods for Neutral Stochastic Delay Differential Equations with Jump Diffusion. Discrete Dynamics in Nature and Society. 2011. Vol. 2011, no. 2011, pp.1-22.
https://search.emarefa.net/detail/BIM-508005
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-508005