Stability of stochastic differential equations with Markovian switching

Research output: Contribution to journalArticle

559 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.

LanguageEnglish
Pages45-67
Number of pages23
JournalStochastic Processes and their Applications
Volume79
Issue number1
DOIs
Publication statusPublished - 1 Jan 1999

Fingerprint

Markovian Switching
Stochastic Equations
Differential equations
Differential equation
Jump Linear Systems
Automatic Control
Exponential Stability
Asymptotic stability
Semilinear
Linear systems
Stochastic differential equations

Keywords

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

Cite this

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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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Stability of stochastic differential equations with Markovian switching. / Mao, Xuerong.

In: Stochastic Processes and their Applications, Vol. 79, No. 1, 01.01.1999, p. 45-67.

Research output: Contribution to journalArticle

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