Abstract and Applied Analysis

Almost Sure and L p Convergence of Split-Step Backward Euler Method for Stochastic Delay Differential Equation

Qian Guo and Xueyin Tao

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Abstract

The convergence of the split-step backward Euler (SSBE) method applied to stochastic differential equation with variable delay is proven in L p -sense. Almost sure convergence is derived from the L p convergence by Chebyshev’s inequality and the Borel-Cantelli lemma; meanwhile, the convergence rate is obtained.

Article information

Source
Abstr. Appl. Anal., Volume 2014 (2014), Article ID 390418, 7 pages.

Dates
First available in Project Euclid: 2 October 2014

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1412277037

Digital Object Identifier
doi:10.1155/2014/390418

Mathematical Reviews number (MathSciNet)
MR3219367

Zentralblatt MATH identifier
07022289

Citation

Guo, Qian; Tao, Xueyin. Almost Sure and ${L}^{p}$ Convergence of Split-Step Backward Euler Method for Stochastic Delay Differential Equation. Abstr. Appl. Anal. 2014 (2014), Article ID 390418, 7 pages. doi:10.1155/2014/390418. https://projecteuclid.org/euclid.aaa/1412277037


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