Stochastic versions of the LaSalle theorem

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198 Citations (Scopus)


The main aim of this paper is to establish stochastic versions of the well-known LaSalle stability theorem. From these stochastic versions follow many classical results on stochastic stability. This shows clearly the power of our new results.

Original languageEnglish
Pages (from-to)175-195
Number of pages21
JournalJournal of Differential Equations
Issue number1
Publication statusPublished - 20 Mar 1999


  • Itô's formula
  • LaSalle's theorem
  • Lyapunov function
  • supermartingale convergence theorem


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