We consider initial point processes $A_0$ on $Z^d$ where $A_0(x), x \in Z^d$ are independent and satisfy certain technical conditions. The particles initially present are assumed to be translated independently according to recurrent random walks. Various limit theorems are then proved involving $S_n(B)$--the total occupation time of $\mathbf{B}$ by time $n$, and $L_n(\mathbf{B})$--the number of distinct particles in $\mathscr{B}$ by time $n$.
Publié le : 1975-10-14
Classification:
Infinite particle systems,
random walks,
central limit theorem,
law of large numbers,
60F05,
60F15,
60J15
@article{1176996262,
author = {Port, S. C. and Stone, C. J. and Weiss, N. A.},
title = {SLLNs and CLTs for Infinite Particle Systems},
journal = {Ann. Probab.},
volume = {3},
number = {6},
year = {1975},
pages = { 753-761},
language = {en},
url = {http://dml.mathdoc.fr/item/1176996262}
}
Port, S. C.; Stone, C. J.; Weiss, N. A. SLLNs and CLTs for Infinite Particle Systems. Ann. Probab., Tome 3 (1975) no. 6, pp. 753-761. http://gdmltest.u-ga.fr/item/1176996262/