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

Lichao Feng, Shoumei Li, Xuerong Mao

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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.
Original languageEnglish
JournalJournal of the Franklin Institute
Publication statusAccepted/In press - 18 Sep 2016

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

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