Lyapunov functions and almost sure exponential stability of stochastic differential equations based on semimartingales with spatial parameters

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Abstract

The objective of this paper is to use the Lyapunov function to study the almost sure exponential stability of the stochastic differential equation Φt = x + ∫0t F(Φs, ds), where F(x, t) is a continuous C-semimartingale with spatial parameter x. This equation includes many important stochastic systems, for example, the classical Ito equation. More importantly, the result can be employed to study the bound of the Lyapunov exponent of stochastic flows.

LanguageEnglish
Pages1481-1490
Number of pages10
JournalSIAM Journal on Control and Optimization
Volume28
Issue number6
DOIs
Publication statusPublished - 1 Nov 1990

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Almost Sure Exponential Stability
Stochastic systems
Semimartingale
Lyapunov functions
Asymptotic stability
Lyapunov Function
Stochastic Equations
Differential equations
Differential equation
Stochastic Flow
Stochastic Systems
Lyapunov Exponent

Keywords

  • mathematical methods
  • differential equations
  • exponential stability
  • Lyapunov functions
  • stochastic differential equations
  • system stability
  • riccati equation
  • sensitivity
  • stabilizability
  • computable bonds

Cite this

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abstract = "The objective of this paper is to use the Lyapunov function to study the almost sure exponential stability of the stochastic differential equation Φt = x + ∫0t F(Φs, ds), where F(x, t) is a continuous C-semimartingale with spatial parameter x. This equation includes many important stochastic systems, for example, the classical Ito equation. More importantly, the result can be employed to study the bound of the Lyapunov exponent of stochastic flows.",
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AB - The objective of this paper is to use the Lyapunov function to study the almost sure exponential stability of the stochastic differential equation Φt = x + ∫0t F(Φs, ds), where F(x, t) is a continuous C-semimartingale with spatial parameter x. This equation includes many important stochastic systems, for example, the classical Ito equation. More importantly, the result can be employed to study the bound of the Lyapunov exponent of stochastic flows.

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KW - computable bonds

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