The present paper deals with the asymptotic behavior of the solution of the
perturbed stochastic hereditary differential equation of the Ito type, by
comparing it in the (2m)(th) moment sense with the solution of the appropri
ate unperturbed equation, on finite intervals or on intervals whose length
tends to infinity. The problems are considered by using the concept of a ra
ndom integral contractor, which includes the Lipschitz condition as a speci
al case. (C) 2001 Elsevier Science Ltd. All rights reserved.