Multi-step Maruyama methods for stochastic delay differential equations

Evelyn Buckwar; Renate Winkler

doi:10.1080/07362990701540311

Multi-step Maruyama methods for stochastic delay differential equations

Evelyn Buckwar
, Renate Winkler

Institute of Stochastics

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

Abstract

In this article the numerical approximation of solutions of Itô stochastic delay differential equations is considered. We construct stochastic linear multi-step Maruyama methods and develop the fundamental numerical analysis concerning their p -consistency, numerical p -stability and p -convergence. For the special case of two-step Maruyama schemes we derive conditions guaranteeing their mean-square consistency.

Original language	English
Pages (from-to)	933-959
Number of pages	27
Journal	Stochastic Analysis and Applications
Volume	25
Issue number	5
DOIs	https://doi.org/10.1080/07362990701540311
Publication status	Published - Sept 2007

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)

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10.1080/07362990701540311

Cite this

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title = "Multi-step Maruyama methods for stochastic delay differential equations",

abstract = "In this article the numerical approximation of solutions of It{\^o} stochastic delay differential equations is considered. We construct stochastic linear multi-step Maruyama methods and develop the fundamental numerical analysis concerning their p -consistency, numerical p -stability and p -convergence. For the special case of two-step Maruyama schemes we derive conditions guaranteeing their mean-square consistency.",

author = "Evelyn Buckwar and Renate Winkler",

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T1 - Multi-step Maruyama methods for stochastic delay differential equations

AU - Buckwar, Evelyn

AU - Winkler, Renate

PY - 2007/9

Y1 - 2007/9

N2 - In this article the numerical approximation of solutions of Itô stochastic delay differential equations is considered. We construct stochastic linear multi-step Maruyama methods and develop the fundamental numerical analysis concerning their p -consistency, numerical p -stability and p -convergence. For the special case of two-step Maruyama schemes we derive conditions guaranteeing their mean-square consistency.

AB - In this article the numerical approximation of solutions of Itô stochastic delay differential equations is considered. We construct stochastic linear multi-step Maruyama methods and develop the fundamental numerical analysis concerning their p -consistency, numerical p -stability and p -convergence. For the special case of two-step Maruyama schemes we derive conditions guaranteeing their mean-square consistency.

UR - https://www.scopus.com/pages/publications/34548450855

U2 - 10.1080/07362990701540311

DO - 10.1080/07362990701540311

M3 - Article

SN - 0736-2994

VL - 25

SP - 933

EP - 959

JO - Stochastic Analysis and Applications

JF - Stochastic Analysis and Applications

IS - 5

ER -

Multi-step Maruyama methods for stochastic delay differential equations

Abstract

Fields of science

JKU Focus areas

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Cite this