ICM 1998, Berlin, Aug. 18–27

Abstracts of Short Communications and Posters

Section:

12. Probability and Statistics

1991 MS Classification: 60 Kolomiets, Yuriy V., Institute of Applied Mathematics and Mechanics, Ukraine On behavior of solutions of evolution equations perturbed by random processes We consider evolution equations of parabolic type, which coefficients are perturbed by the stochastic processes and depend from a small parameter. We prove the statements of the type of the Central Limit Theorem for different characters of the dependence from a small parameter for certain stochastic processes at a small parameter tends to zero. We also investigate the case of the non-fulfillment of the balance condition in the diffusion approximation scheme. In the limit we obtain stochastic evolution equations with certain coefficients. This coefficients depend from coefficients of initial equation and characteristics of a perturbing processes.