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Limit theorems for stationary random evolutions

Authors:	Joseph C Watkins

Institution:	Department of Mathematics, University of British Columbia, Vancouver, British Columbia V6T 1Y4, Canada

Abstract:	On a separable Banach space, let A(ξ₁),A(ξ₂),... be a strictly stationary sequence of infinitesimal operators, centered so that EA(ξ_i) = 0, i = 1,2,.... This paper characterizes the limit of the random evolutions $Y_{n} (t)=exp 1 n A(ξ_{n^{2}t]}) ?exp 1 n A(ξ_{2}) exp 1 n A(ξ_{1}) Y_{n} (0)$ as the solution to a martingale problem. This work is a direct extension of previous work on i.i.d. random evolutions.

Keywords:	random evolution central limit theorem law of large numbers martingale problem stationary process mixing
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