Stability of stochastic differential equations with Markovian switching

Xuerong Mao

doi:10.1016/S0304-4149(98)00070-2

Stability of stochastic differential equations with Markovian switching

Xuerong Mao^*

^*Corresponding author for this work

Mathematics And Statistics

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

732 Citations (Scopus)

Abstract

Stability of stochastic differential equations with Markovian switching has recently received a lot of attention. For example, stability of linear or semi-linear type of such equations has been studied by Basak et al. (1996, J. Math. Anal. Appl. 202, 604-622), Ji and Chizeck (1990, Automat. Control 35, 777-788) and Mariton (1990, Jump Linear Systems in Automatic Control, Marcel Dekker, New York). The aim of this paper is to discuss the exponential stability for general nonlinear stochastic differential equations with Markovian switching.

Original language	English
Pages (from-to)	45-67
Number of pages	23
Journal	Stochastic Processes and their Applications
Volume	79
Issue number	1
DOIs	https://doi.org/10.1016/S0304-4149(98)00070-2
Publication status	Published - 1 Jan 1999

Keywords

Brownian motion
generalized Itô's formula
Lyapunov exponent
M-matrix
Markov chain generator

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abstract = "Stability of stochastic differential equations with Markovian switching has recently received a lot of attention. For example, stability of linear or semi-linear type of such equations has been studied by Basak et al. (1996, J. Math. Anal. Appl. 202, 604-622), Ji and Chizeck (1990, Automat. Control 35, 777-788) and Mariton (1990, Jump Linear Systems in Automatic Control, Marcel Dekker, New York). The aim of this paper is to discuss the exponential stability for general nonlinear stochastic differential equations with Markovian switching.",

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AB - Stability of stochastic differential equations with Markovian switching has recently received a lot of attention. For example, stability of linear or semi-linear type of such equations has been studied by Basak et al. (1996, J. Math. Anal. Appl. 202, 604-622), Ji and Chizeck (1990, Automat. Control 35, 777-788) and Mariton (1990, Jump Linear Systems in Automatic Control, Marcel Dekker, New York). The aim of this paper is to discuss the exponential stability for general nonlinear stochastic differential equations with Markovian switching.

KW - Brownian motion

KW - generalized Itô's formula

KW - Lyapunov exponent

KW - M-matrix

KW - Markov chain generator

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Stability of stochastic differential equations with Markovian switching

Abstract

Keywords

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