Lyapunov exponents of hybrid stochastic heat equations

J. H. Bao; X. R. Mao; C. G. Yuan

doi:10.1016/j.sysconle.2011.10.009

Lyapunov exponents of hybrid stochastic heat equations

J. H. Bao, X. R. Mao, C. G. Yuan

Mathematics And Statistics

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

12 Citations (Scopus)

Abstract

In this paper, we investigate a class of hybrid stochastic heat equations. By explicit formulae of solutions, we not only reveal the sample Lyapunov exponents but also discuss the pth moment Lyapnov exponents. Moreover, several examples are established to demonstrate that unstable (deterministic or stochastic) dynamical systems can be stabilized by Markovian switching.

Original language	English
Pages (from-to)	165-172
Number of pages	8
Journal	Systems and Control Letters
Volume	61
Issue number	1
DOIs	https://doi.org/10.1016/j.sysconle.2011.10.009
Publication status	Published - Jan 2012

Keywords

diffusion
partial differential equation
stabilization
stochastic heat equation
Lyapunov exponent
Markov chain
large deviation

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10.1016/j.sysconle.2011.10.009

Cite this

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title = "Lyapunov exponents of hybrid stochastic heat equations",

abstract = "In this paper, we investigate a class of hybrid stochastic heat equations. By explicit formulae of solutions, we not only reveal the sample Lyapunov exponents but also discuss the pth moment Lyapnov exponents. Moreover, several examples are established to demonstrate that unstable (deterministic or stochastic) dynamical systems can be stabilized by Markovian switching.",

keywords = "diffusion, partial differential equation, stabilization, stochastic heat equation, Lyapunov exponent, Markov chain, large deviation",

author = "Bao, {J. H.} and Mao, {X. R.} and Yuan, {C. G.}",

year = "2012",

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AU - Bao, J. H.

AU - Mao, X. R.

AU - Yuan, C. G.

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N2 - In this paper, we investigate a class of hybrid stochastic heat equations. By explicit formulae of solutions, we not only reveal the sample Lyapunov exponents but also discuss the pth moment Lyapnov exponents. Moreover, several examples are established to demonstrate that unstable (deterministic or stochastic) dynamical systems can be stabilized by Markovian switching.

AB - In this paper, we investigate a class of hybrid stochastic heat equations. By explicit formulae of solutions, we not only reveal the sample Lyapunov exponents but also discuss the pth moment Lyapnov exponents. Moreover, several examples are established to demonstrate that unstable (deterministic or stochastic) dynamical systems can be stabilized by Markovian switching.

KW - diffusion

KW - partial differential equation

KW - stabilization

KW - stochastic heat equation

KW - Lyapunov exponent

KW - Markov chain

KW - large deviation

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DO - 10.1016/j.sysconle.2011.10.009

M3 - Article

VL - 61

SP - 165

EP - 172

JO - Systems and Control Letters

JF - Systems and Control Letters

SN - 0167-6911

IS - 1

ER -

Lyapunov exponents of hybrid stochastic heat equations

Abstract

Keywords

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