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October, 1976 Ergodic Theorems for an Infinite Particle System with Births and Deaths
Diane Schwartz
Ann. Probab. 4(5): 783-801 (October, 1976). DOI: 10.1214/aop/1176995984


Let $p(x, y)$ be an irreducible symmetric transition function for a Markov chain on a countable set $S$. Let $\eta_t$ be the infinite particle system on $S$ with simple exclusion interaction modified to allow the spontaneous creation and destruction of particles in the system. A complete characterization of the invariant probability measures for this system is obtained in the case where the exponential rates of creation and destruction are independent of the configuration of the system. Furthermore, if $\mathscr{M}$ is the set of probability measures on the state space of $\eta_t$ and $S(t)$ is the semigroup on $\mathscr{M}$ determined by $$S(t)\mu(A) = \int P^\eta\lbrack\eta_t \in A\rbrack d\mu(\eta)$$ theorems concerning the weak convergence of $S(t)\mu$ to the invariant measures of $\eta_t$ are proved.


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Diane Schwartz. "Ergodic Theorems for an Infinite Particle System with Births and Deaths." Ann. Probab. 4 (5) 783 - 801, October, 1976.


Published: October, 1976
First available in Project Euclid: 19 April 2007

zbMATH: 0357.60050
MathSciNet: MR418293
Digital Object Identifier: 10.1214/aop/1176995984

Primary: 60K35

Keywords: ergodic theorems , infinite particle systems , Invariant measures

Rights: Copyright © 1976 Institute of Mathematical Statistics


Vol.4 • No. 5 • October, 1976
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