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Singularly perturbed stochastic differential equations with dynamical limits. (English) Zbl 0841.60043
Corduneanu, C. (ed.), Qualitative problems for differential equations and control theory. Dedicated to Aristide Halanay on occasion of his 70th birthday. Singapore: World Scientific. 301-311 (1995).
The authors prove that the dynamical limits of singularly perturbed stochastic differential equations are found in the class of a set of probability measures which are invariant measures associated with the corresponding stochastic flow. This work is a stochastic version of the result by A. N. Tikhonov [Mat. Sbornik, n. Ser. 31(73), 575-586 (1952; Zbl 0048.07101)].
For the entire collection see [Zbl 0838.00012].
Reviewer: J.H.Kim (Pusan)
60H10 Stochastic ordinary differential equations (aspects of stochastic analysis)