## The Annals of Probability

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

### SLLNs and CLTs for Infinite Particle Systems

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

#### 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