Ukrainian Mathematical Bulletin

Volume 1, Issue 2, 2004 pp. 251-264.

Preservation of the Convergence of Solutions of Stochastic Equations under the Perturbation of Their Coefficients

Authors: S.Ya.Makhno
Author institution: Institute of Applied Mathematics and Mechanics of the Ukrainian National Academy of Sciences

Summary: We consider solutions of It\^o stochastic equations whose coefficients depend irregularly on a small parameter as this parameter tends to zero. We present conditions for the convergence of these solutions in the distribution sense to a solution of an It\^o stochastic equation. Then the coefficients of the original equations are perturbed by functions that also depend on a small parameter. We establish conditions for the weak convergence of solutions of the stochastic equations with perturbed coefficients to the same limit process.

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