Homogenization of random functionals on solutions of stochastic equations

Abstract

The paper deals with an integral functional on a stationary random mixing field and on a solution of the stochastic equation which depend on a small parameter. The type of the functional is conditioned by the probabilistic representation of solutions of the Cauchy problem and the first boundaryvalue problem for a linear second-order parabolic equation in a nondivergent form with unbounded quick random oscillations of the zero-order term of the derivative. The central limit theorem of convergence of the functional is proved.