Open Access
April, 1976 On a Class of Set-Valued Markov Processes
T. E. Harris
Ann. Probab. 4(2): 175-194 (April, 1976). DOI: 10.1214/aop/1176996129


Let $Z$ be a finite or countable set, $\Xi$ the set of subsets of $Z, \{\xi_t\}$ a Markov process with state space $\Xi$. A process $\{\xi_t^\ast\}$ with the same state space is called associate to $\{\xi_t\}$ if $\mathbf{P}_\xi\{\xi_t \cap \eta \neq \varnothing\} = \mathbf{P}_\eta^\ast\{\xi_t^\ast \cap \xi \neq \varnothing\}$ whenever $\xi$ and $\eta$ are subsets of $\mathbf{Z}$, at least one of which is finite. Criteria are found for the existence of a process associate to a given one. Examples and applications are given.


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T. E. Harris. "On a Class of Set-Valued Markov Processes." Ann. Probab. 4 (2) 175 - 194, April, 1976.


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

zbMATH: 0357.60049
MathSciNet: MR400468
Digital Object Identifier: 10.1214/aop/1176996129

Primary: 60K35

Keywords: association , interaction , set-valued process

Rights: Copyright © 1976 Institute of Mathematical Statistics

Vol.4 • No. 2 • April, 1976
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