Perturbed stochastic hereditary differential equations with integral contractors

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 appropriate unperturbed equation, on finite intervals or on intervals whose length tends to infinity. The problems are considered by using the concept of a random integral contractor, which includes the Lipschitz condition as a special case.