On properties of solutions of stochastic equations: Asymptotic normality and large deviations

Abstract

Let x(t) be a solution of a stochastic equation with periodic and perturbance coefficients. The perturbance process is a jump process with a finite set of values. We study the asymptotic behavior of x(t) as t→∞. The property of asymptotic normality and the large deviation principle are the main results in this paper

Keywords:

• Stochastic equation
• asymptotic normality
• large deviation principle
• Mathematics Subject Classification 1991: 60F10, 60H10