Stochastic versions of the LaSalle theorem

Mao, X. (1999) Stochastic versions of the LaSalle theorem. Journal of Differential Equations, 153 (1). pp. 175-195. ISSN 0022-0396 (https://doi.org/10.1006/jdeq.1998.3552)

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Abstract

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.