On existence and uniqueness of solution of stochastic differential equations with heredity

We consider the Cauchy problem for the stochastic differential equation with the heredity where x _t(s) = x(s)for s?(- ∞,t).Existence and uniqueness theorems for the problem (1),(2)are proved inthe case,when instead of the Lipschitz condition for the functions a(t,u) and b(t,u)on u someless restrictive conditions (Ousgood or Hölder type)are satisfied, and the operator(Fx)(t) = x(t)-f(t,x _t) is invertible.Similar questions were considered in1-4]