Convergence of the Euler Method of Stochastic Differential Equations with Piecewise Continuous Arguments

Ling Zhang and Minghui Song

Abstract and Applied Analysis, 2012, vol. 2012, 1-16

Abstract:

The main purpose of this paper is to investigate the strong convergence of the Euler method to stochastic differential equations with piecewise continuous arguments (SEPCAs). Firstly, it is proved that the Euler approximation solution converges to the analytic solution under local Lipschitz condition and the bounded th moment condition. Secondly, the Euler approximation solution converge to the analytic solution is given under local Lipschitz condition and the linear growth condition. Then an example is provided to show which is satisfied with the monotone condition without the linear growth condition. Finally, the convergence of numerical solutions to SEPCAs under local Lipschitz condition and the monotone condition is established.

Date: 2012
References: Add references at CitEc
Citations: View citations in EconPapers (1)

Downloads: (external link)
http://downloads.hindawi.com/journals/AAA/2012/643783.pdf (application/pdf)
http://downloads.hindawi.com/journals/AAA/2012/643783.xml (text/xml)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:hin:jnlaaa:643783

DOI: 10.1155/2012/643783

Access Statistics for this article

More articles in Abstract and Applied Analysis from Hindawi
Bibliographic data for series maintained by Mohamed Abdelhakeem ().