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Razumikhin-Type Theorems of Infinite Dimensional Stochastic Functional Differential Equations

  • Kai Liu
  • Yufeng Shi
Part of the IFIP International Federation for Information Processing book series (IFIPAICT, volume 202)

Abstract

The argument of Razumikhin-type has been well developed and showed significant advantage for the stability of stochastic functional differential equations in finite dimensions. However, so far there have been almost no results of Razumikhin-type on the stability of mild solutions of stochastic functional differential equations in infinite dimensions. The main aim of this paper is to establish Razumikhin-type stability theorems for stochastic functional differential equations in infinite dimensions. By virtue of these new criteria, we can establish the exponential stability of stochastic delay differential equations and stochastic delay partial differential equations.

Key words

Lyapunov function Razumikhin-type theorem Stochastic functional differential equations in infinite dimensions 

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Copyright information

© International Federation for Information Processing 2006

Authors and Affiliations

  • Kai Liu
    • 1
  • Yufeng Shi
    • 2
  1. 1.Department of Mathematical SciencesThe University of LiverpoolLiverpoolUK
  2. 2.School of Mathematics and System SciencesShandong UniversityJinanChina

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