The Annals of Probability

SLLNs and CLTs for Infinite Particle Systems

S. C. Port, C. J. Stone, and N. A. Weiss

Full-text: Open access

Abstract

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 $n$.

Article information

Source
Ann. Probab., Volume 3, Number 5 (1975), 753-761.

Dates
First available in Project Euclid: 19 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aop/1176996262

Digital Object Identifier
doi:10.1214/aop/1176996262

Mathematical Reviews number (MathSciNet)
MR408044

Zentralblatt MATH identifier
0335.60039

JSTOR
links.jstor.org

Subjects
Primary: 60F05: Central limit and other weak theorems
Secondary: 60F15: Strong theorems 60J15

Keywords
Infinite particle systems random walks central limit theorem law of large numbers

Citation

Port, S. C.; Stone, C. J.; Weiss, N. A. SLLNs and CLTs for Infinite Particle Systems. Ann. Probab. 3 (1975), no. 5, 753--761. doi:10.1214/aop/1176996262. https://projecteuclid.org/euclid.aop/1176996262


Export citation