Numerical analysis of explicit one-step methods for stochastic delay differential equations

Evelyn Buckwar; Christopher T.H. Baker

doi:10.1112/s1461157000000322

Numerical analysis of explicit one-step methods for stochastic delay differential equations

Evelyn Buckwar, Christopher T.H. Baker

Institute of Stochastics

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

Abstract

We consider the problem of strong approximations of the solution of stochastic differential equations of Itô form with a constant lag in the argument. We indicate the nature of the equations of interest, and give a convergence proof in full detail for explicit one-step methods. We provide some illustrative numerical examples, using the Euler–Maruyama scheme.

Original language	English
Pages (from-to)	315-335
Number of pages	21
Journal	LMS Journal of Computation and Mathematics
Volume	3
DOIs	https://doi.org/10.1112/s1461157000000322
Publication status	Published - 2000

Fields of science

101002 Analysis
101029 Mathematical statistics
101014 Numerical mathematics
101024 Probability theory
101015 Operations research
101026 Time series analysis
101019 Stochastics
107 Other Natural Sciences
211 Other Technical Sciences

JKU Focus areas

Computation in Informatics and Mathematics
Engineering and Natural Sciences (in general)

Access to Document

10.1112/s1461157000000322

Cite this

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abstract = "We consider the problem of strong approximations of the solution of stochastic differential equations of It{\^o} form with a constant lag in the argument. We indicate the nature of the equations of interest, and give a convergence proof in full detail for explicit one-step methods. We provide some illustrative numerical examples, using the Euler–Maruyama scheme.",

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AB - We consider the problem of strong approximations of the solution of stochastic differential equations of Itô form with a constant lag in the argument. We indicate the nature of the equations of interest, and give a convergence proof in full detail for explicit one-step methods. We provide some illustrative numerical examples, using the Euler–Maruyama scheme.

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DO - 10.1112/s1461157000000322

M3 - Article

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JO - LMS Journal of Computation and Mathematics

JF - LMS Journal of Computation and Mathematics

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