2017
Том 69
№ 7

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 $p - 1$.

English version (Springer): Ukrainian Mathematical Journal 58 (2006), no. 12, pp 1799-1817.

Citation Example: Bondarev B. V., Kovtun E. E. 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 // Ukr. Mat. Zh. - 2006. - 58, № 12. - pp. 1587–1601.

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