Open Access
May, 1984 A Central Limit Problem in Random Evolutions
Joseph C. Watkins
Ann. Probab. 12(2): 480-513 (May, 1984). DOI: 10.1214/aop/1176993302


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.


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Joseph C. Watkins. "A Central Limit Problem in Random Evolutions." Ann. Probab. 12 (2) 480 - 513, May, 1984.


Published: May, 1984
First available in Project Euclid: 19 April 2007

zbMATH: 0547.60040
MathSciNet: MR735850
Digital Object Identifier: 10.1214/aop/1176993302

Primary: 60F17
Secondary: 60B10 , 60B12 , 60F05 , 60G44

Keywords: Central limit problem , Duality , Martingale problem , random evolution , weak convergence

Rights: Copyright © 1984 Institute of Mathematical Statistics

Vol.12 • No. 2 • May, 1984
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