Numerical method for stationary distribution of stochastic differential equations with Markovian switching

X. Mao; C. Yuan; G. Yin

doi:10.1016/j.cam.2004.03.016

Numerical method for stationary distribution of stochastic differential equations with Markovian switching

X. Mao, C. Yuan, G. Yin

Mathematics And Statistics

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

37 Citations (Scopus)

Abstract

In principle, once the existence of the stationary distribution of a stochastic differential equation with Markovian switching is assured, we may compute it by solving the associated system of the coupled Kolmogorov-Fokker-Planck equations. However, this is nontrivial in practice. As a viable alternative, we use the Euler-Maruyama scheme to obtain the stationary distribution in this paper.

Original language	English
Pages (from-to)	1-27
Number of pages	26
Journal	Journal of Computational and Applied Mathematics
Volume	174
Issue number	1
DOIs	https://doi.org/10.1016/j.cam.2004.03.016
Publication status	Published - Feb 2005

Keywords

Brownian motion
stationary distribution
Lipschitz condition
Markov chain
stochastic differential equations
Euler-Maruyama methods
weak convergence to stationary measures

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10.1016/j.cam.2004.03.016

Cite this

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title = "Numerical method for stationary distribution of stochastic differential equations with Markovian switching",

abstract = "In principle, once the existence of the stationary distribution of a stochastic differential equation with Markovian switching is assured, we may compute it by solving the associated system of the coupled Kolmogorov-Fokker-Planck equations. However, this is nontrivial in practice. As a viable alternative, we use the Euler-Maruyama scheme to obtain the stationary distribution in this paper.",

keywords = "Brownian motion, stationary distribution, Lipschitz condition, Markov chain, stochastic differential equations, Euler-Maruyama methods, weak convergence to stationary measures",

author = "X. Mao and C. Yuan and G. Yin",

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AU - Mao, X.

AU - Yuan, C.

AU - Yin, G.

PY - 2005/2

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N2 - In principle, once the existence of the stationary distribution of a stochastic differential equation with Markovian switching is assured, we may compute it by solving the associated system of the coupled Kolmogorov-Fokker-Planck equations. However, this is nontrivial in practice. As a viable alternative, we use the Euler-Maruyama scheme to obtain the stationary distribution in this paper.

AB - In principle, once the existence of the stationary distribution of a stochastic differential equation with Markovian switching is assured, we may compute it by solving the associated system of the coupled Kolmogorov-Fokker-Planck equations. However, this is nontrivial in practice. As a viable alternative, we use the Euler-Maruyama scheme to obtain the stationary distribution in this paper.

KW - Brownian motion

KW - stationary distribution

KW - Lipschitz condition

KW - Markov chain

KW - stochastic differential equations

KW - Euler-Maruyama methods

KW - weak convergence to stationary measures

UR - http://dx.doi.org/10.1016/j.cam.2004.03.016

U2 - 10.1016/j.cam.2004.03.016

DO - 10.1016/j.cam.2004.03.016

M3 - Article

VL - 174

SP - 1

EP - 27

JO - Journal of Computational and Applied Mathematics

JF - Journal of Computational and Applied Mathematics

SN - 0377-0427

IS - 1

ER -

Numerical method for stationary distribution of stochastic differential equations with Markovian switching

Abstract

Keywords

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