Convergence of numerical solutions to neutral stochastic delay differential equations with Markovian switching

Shaobo Zhou; Fuke Wu

doi:10.1016/j.cam.2008.10.013

Convergence of numerical solutions to neutral stochastic delay differential equations with Markovian switching

Shaobo Zhou, Fuke Wu

Research output: Contribution to journal › Article › Research › peer-review

46 Citations (Scopus)

Abstract

Recently, numerical solutions of stochastic differential equations have received a great deal of attention. It is surprising that there are not any numerical methods established for neutral stochastic delay differential equations yet. In the paper, the Euler-Maruyama method for neutral stochastic delay differential equations is developed. The key aim is to show that the numerical solutions will converge to the true solutions under the local Lipschitz condition.

Original language	English
Pages (from-to)	85 - 96
Number of pages	12
Journal	Journal of Computational and Applied Mathematics
Volume	229
Issue number	1
DOIs	https://doi.org/10.1016/j.cam.2008.10.013
Publication status	Published - 2009
Externally published	Yes

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10.1016/j.cam.2008.10.013

Cite this

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title = "Convergence of numerical solutions to neutral stochastic delay differential equations with Markovian switching",

abstract = "Recently, numerical solutions of stochastic differential equations have received a great deal of attention. It is surprising that there are not any numerical methods established for neutral stochastic delay differential equations yet. In the paper, the Euler-Maruyama method for neutral stochastic delay differential equations is developed. The key aim is to show that the numerical solutions will converge to the true solutions under the local Lipschitz condition.",

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AU - Wu, Fuke

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AB - Recently, numerical solutions of stochastic differential equations have received a great deal of attention. It is surprising that there are not any numerical methods established for neutral stochastic delay differential equations yet. In the paper, the Euler-Maruyama method for neutral stochastic delay differential equations is developed. The key aim is to show that the numerical solutions will converge to the true solutions under the local Lipschitz condition.

U2 - 10.1016/j.cam.2008.10.013

DO - 10.1016/j.cam.2008.10.013

M3 - Article

VL - 229

SP - 85

EP - 96

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JF - Journal of Computational and Applied Mathematics

SN - 0377-0427

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