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Approximation of delay stochastic equations with constant retardation by usual Ito equations. (English) Zbl 0687.60059
Consider the following system of delay stochastic equations $$(1)\quad dx(t)=f(t,x(t),x(t-h))dt+g(t,x(t),x(t-h))dw(t)$$ with the initial conditions $$x(t\sb 0)=\eta,\quad x(t\sb 0+\theta)=\phi (\theta),\quad - h\le \theta <0,$$ where f,g are Lipschitz and satisfy the growth condition, w is Brownian motion, $\eta$ is a random variable and $\phi$ is a stochastic process. By using an approximation result for deterministic hereditary equations by ordinary differential equations, an analogous result is obtained for (1) with the help of Itô equations.
Reviewer: C.Tudor

##### MSC:
 60H20 Stochastic integral equations