Abstract

Interest has been growing in the investigation of systems of integrodifferential equations with random perturbations. In [i], on the basis of an assumption about the existence of a slowly varying solution [2], and on the basis of the statistical linearization method [3], a stochastic integrodifferential second-order equation is approximated by a stochastic differential equation. The asymptotic methods of Krylov-Bogolyubov--Mitropol'skii and the method of equations of Kolmogorov-Fokker-Planck (KFP) [4-8] are applicable to the latter. In the present article we consider the analogous problem for quasilinear systems of stochastic integrodifferential first-order equations. We investigate the problem of the mathematical basis of the proposed procedures.