Abstract
Let $\{T_n\}_{n \geq 1}$ be a sequence of independent and identically distributed strongly continuous semigroups on a separable Banach space. The corresponding generators $\{A_n\}_{n \geq 1}$ satisfy $E\lbrack A_n\rbrack = 0$. Conditions are given to guarantee that the weak limit $Y(t) = \text{limit}_{n \rightarrow \infty} \prod^{\lbrack n^2t\rbrack}_{i = 1} T_i(1/n) Y_n(0)$ exists, and is characterized as the unique solution of a martingale problem. Transport phenomena, random classical mechanics, and families of bounded operators are the featured examples.
Citation
Joseph C. Watkins. "A Central Limit Problem in Random Evolutions." Ann. Probab. 12 (2) 480 - 513, May, 1984. https://doi.org/10.1214/aop/1176993302
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