Numerical Solutions of Stochastic Differential Equations with Piecewise Continuous Arguments under Khasminskii-Type Conditions
Joint Authors
Source
Journal of Applied Mathematics
Issue
Vol. 2012, Issue 2012 (31 Dec. 2012), pp.1-21, 21 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2012-07-04
Country of Publication
Egypt
No. of Pages
21
Main Subjects
Abstract EN
The main purpose of this paper is to investigate the convergence of the Euler method to stochastic differential equations with piecewise continuous arguments (SEPCAs).
The classical Khasminskii-type theorem gives a powerful tool to examine the global existence of solutions for stochastic differential equations (SDEs) without the linear growth condition by the use of the Lyapunov functions.
However, there is no such result for SEPCAs.
Firstly, this paper shows SEPCAs which have nonexplosion global solutions under local Lipschitz condition without the linear growth condition.
Then the convergence in probability of numerical solutions to SEPCAs under the same conditions is established.
Finally, an example is provided to illustrate our theory.
American Psychological Association (APA)
Song, Minghui& Zhang, Ling. 2012. Numerical Solutions of Stochastic Differential Equations with Piecewise Continuous Arguments under Khasminskii-Type Conditions. Journal of Applied Mathematics،Vol. 2012, no. 2012, pp.1-21.
https://search.emarefa.net/detail/BIM-1028977
Modern Language Association (MLA)
Song, Minghui& Zhang, Ling. Numerical Solutions of Stochastic Differential Equations with Piecewise Continuous Arguments under Khasminskii-Type Conditions. Journal of Applied Mathematics No. 2012 (2012), pp.1-21.
https://search.emarefa.net/detail/BIM-1028977
American Medical Association (AMA)
Song, Minghui& Zhang, Ling. Numerical Solutions of Stochastic Differential Equations with Piecewise Continuous Arguments under Khasminskii-Type Conditions. Journal of Applied Mathematics. 2012. Vol. 2012, no. 2012, pp.1-21.
https://search.emarefa.net/detail/BIM-1028977
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1028977