Asymptotic stability and boundedness of stochastic functional differential equations with Markovian switching

Lichao Feng, Shoumei Li, Xuerong Mao

Research output: Contribution to journalArticle

Abstract

This paper is concerned with the boundedness, exponential stability and almost sure asymptotic stability of stochastic functional differential equations (SFDEs) with Markovian switching. The key technique used is the method of multiple Lyapunov functions. We use two auxiliary functions to dominate the corresponding different Lyapunov function in different mode while the diffusion operator in different model is controlled by other multiple auxiliary functions. Our conditions on the diffusion operator are weaker than those in the related existing works.
LanguageEnglish
JournalJournal of the Franklin Institute
Publication statusAccepted/In press - 18 Sep 2016

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Stochastic Functional Differential Equations
Markovian Switching
Auxiliary Function
Lyapunov functions
Asymptotic stability
Asymptotic Stability
Mathematical operators
Boundedness
Differential equations
Almost Sure Stability
Multiple Lyapunov Functions
Operator
Exponential Stability
Lyapunov Function
Model

Keywords

  • stichastic functional differential equations
  • Markovian switching
  • asymptotic stability
  • boundedness
  • generalized Itô's formula
  • dynamic systems
  • stability theory
  • models
  • exponential stability
  • Lyapunov functions
  • diffusion operator

Cite this

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AB - This paper is concerned with the boundedness, exponential stability and almost sure asymptotic stability of stochastic functional differential equations (SFDEs) with Markovian switching. The key technique used is the method of multiple Lyapunov functions. We use two auxiliary functions to dominate the corresponding different Lyapunov function in different mode while the diffusion operator in different model is controlled by other multiple auxiliary functions. Our conditions on the diffusion operator are weaker than those in the related existing works.

KW - stichastic functional differential equations

KW - Markovian switching

KW - asymptotic stability

KW - boundedness

KW - generalized Itô's formula

KW - dynamic systems

KW - stability theory

KW - models

KW - exponential stability

KW - Lyapunov functions

KW - diffusion operator

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