Order reduction for a system of stochastic differential equations with a small parameter in the coefficient of the leading derivative. Estimate for the rate of convergence

Abstract

In the metric $\rho(X, Y) = (\sup\limits_{0 \leq t \leq T} M|X(t) - Y(t)|^2)^{1/2} $ for an ordinary stochastic differential equation of order $p \geq 2$ with small parameter of the higher derivative, we establish an estimate of the rate of convergence of its solution to a solution of stochastic equation of order $p - 1$.