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October, 1975 SLLNs and CLTs for Infinite Particle Systems
S. C. Port, C. J. Stone, N. A. Weiss
Ann. Probab. 3(5): 753-761 (October, 1975). DOI: 10.1214/aop/1176996262

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 $n$.

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S. C. Port. C. J. Stone. N. A. Weiss. "SLLNs and CLTs for Infinite Particle Systems." Ann. Probab. 3 (5) 753 - 761, October, 1975. https://doi.org/10.1214/aop/1176996262

Information

Published: October, 1975
First available in Project Euclid: 19 April 2007

zbMATH: 0335.60039
MathSciNet: MR408044
Digital Object Identifier: 10.1214/aop/1176996262

Subjects:
Primary: 60F05
Secondary: 60F15 , 60J15

Keywords: central limit theorem , infinite particle systems , Law of Large Numbers , Random walks

Rights: Copyright © 1975 Institute of Mathematical Statistics

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Vol.3 • No. 5 • October, 1975
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