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On some stability properties of stochastic differential equations of Itô’s type. (English) Zbl 0625.60066

The author deals with stability of strong solutions for the SDE \[ d\zeta_ t=b(t,\zeta_ t)dt+\sigma (t,\zeta_ t)dW_ t. \] The distance between two solutions is described by a suitable function \(\rho\) (t,x,y). Conditions for stability are given in terms of appropriate Lyapunov-functions.
Reviewer: D.Beyer

MSC:

60H10 Stochastic ordinary differential equations (aspects of stochastic analysis)
93E15 Stochastic stability in control theory
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