Averaging in parabolic systems subjected to weakly dependent random disturbances. $L_1$-approach

Abstract

One considers an averaging method in equations of parabolic type, situated under the action of centered, weakly dependent random perturbations so that their integrals, normalized in an appropriate manner, satisfy S. N. Bernshtein's exponential estimate. For normalized fluctuations of the solution of the initial equation relative to the solution of the averaged equation, which turns out to be deterministic, one has established S. N. Bernshtein's exponential estimates. On the basis of the obtained inequalities, for an arbitrary prescribed confidence level, one can indicate a confidence band, whose bounds are determined by the solving of the averaged equation, which contains the solution of the initial problem.