Split-step Milstein methods for multi-channel stiff stochastic differential systems

V. Reshniak; A. Q.M. Khaliq; D. A. Voss; G. Zhang

doi:10.1016/j.apnum.2014.10.005

Split-step Milstein methods for multi-channel stiff stochastic differential systems

V. Reshniak, A. Q.M. Khaliq, D. A. Voss, G. Zhang

Data Analysis and Machine Learning

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25 Scopus citations

Abstract

We consider split-step Milstein methods for the solution of stiff stochastic differential equations with an emphasis on systems driven by multi-channel noise. We show their strong order of convergence and investigate mean-square stability properties for different noise and drift structures. The stability matrices are established in a form convenient for analyzing their impact arising from different deterministic drift integrators. Numerical examples are provided to illustrate the effectiveness and reliability of these methods.

Original language	English
Pages (from-to)	1-23
Number of pages	23
Journal	Applied Numerical Mathematics
Volume	89
DOIs	https://doi.org/10.1016/j.apnum.2014.10.005
State	Published - Jan 2015

Keywords

Langevin equations
Mean-square stability
Multi-channel noise
Split-step method
Stiff equations
Stochastic differential equations

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10.1016/j.apnum.2014.10.005

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title = "Split-step Milstein methods for multi-channel stiff stochastic differential systems",

abstract = "We consider split-step Milstein methods for the solution of stiff stochastic differential equations with an emphasis on systems driven by multi-channel noise. We show their strong order of convergence and investigate mean-square stability properties for different noise and drift structures. The stability matrices are established in a form convenient for analyzing their impact arising from different deterministic drift integrators. Numerical examples are provided to illustrate the effectiveness and reliability of these methods.",

keywords = "Langevin equations, Mean-square stability, Multi-channel noise, Split-step method, Stiff equations, Stochastic differential equations",

author = "V. Reshniak and Khaliq, \{A. Q.M.\} and Voss, \{D. A.\} and G. Zhang",

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AU - Khaliq, A. Q.M.

AU - Voss, D. A.

AU - Zhang, G.

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AB - We consider split-step Milstein methods for the solution of stiff stochastic differential equations with an emphasis on systems driven by multi-channel noise. We show their strong order of convergence and investigate mean-square stability properties for different noise and drift structures. The stability matrices are established in a form convenient for analyzing their impact arising from different deterministic drift integrators. Numerical examples are provided to illustrate the effectiveness and reliability of these methods.

KW - Langevin equations

KW - Mean-square stability

KW - Multi-channel noise

KW - Split-step method

KW - Stiff equations

KW - Stochastic differential equations

UR - https://www.scopus.com/pages/publications/84911476361

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DO - 10.1016/j.apnum.2014.10.005

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VL - 89

SP - 1

EP - 23

JO - Applied Numerical Mathematics

JF - Applied Numerical Mathematics

ER -

Split-step Milstein methods for multi-channel stiff stochastic differential systems

Abstract

Keywords

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