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

  • B. V. Bondarev
  • E. E. Kovtun

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 $p - 1$.
Published
25.12.2006
How to Cite
Bondarev, B. V., and E. E. Kovtun. “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”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 58, no. 12, Dec. 2006, pp. 1587–1601, http://umj.imath.kiev.ua/index.php/umj/article/view/3557.
Section
Research articles