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Almost sure polynomial stability for a class of stochastic differential equations. (English) Zbl 0765.60058

This paper concerns the problem of determining whether the solution of a stochastic differential equation approaches zero asymptotically at a polynomial rate almost surely. The method described involves using an appropriate Lyapunov function which, in practice, may be found by considering a Lyapunov function for the corresponding deterministic differential equation. Theorems are proved establishing the desired convergence provided that the Lyapunov function satisfies certain conditions. Some examples are given to illustrate the method.

MSC:

60H10 Stochastic ordinary differential equations (aspects of stochastic analysis)
93E15 Stochastic stability in control theory
34F05 Ordinary differential equations and systems with randomness
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