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.
Publié le : 1984-05-14
Classification:
Central limit problem,
random evolution,
weak convergence,
martingale problem,
duality,
60F17,
60B10,
60B12,
60F05,
60G44
@article{1176993302,
author = {Watkins, Joseph C.},
title = {A Central Limit Problem in Random Evolutions},
journal = {Ann. Probab.},
volume = {12},
number = {4},
year = {1984},
pages = { 480-513},
language = {en},
url = {http://dml.mathdoc.fr/item/1176993302}
}
Watkins, Joseph C. A Central Limit Problem in Random Evolutions. Ann. Probab., Tome 12 (1984) no. 4, pp. 480-513. http://gdmltest.u-ga.fr/item/1176993302/