Open Access
June, 1967 Realization of Stochastic Systems
Michael Arbib
Ann. Math. Statist. 38(3): 927-933 (June, 1967). DOI: 10.1214/aoms/1177698889


Heller has given necessary and sufficient conditions that a stochastic process be induced from a Markov chain. We consider a process induced by a Markov chain to be a probabilistic finite automaton with one input. With each state of a probabilistic finite automaton, we may associate a function $p(u \mid v)$, which tells us the probability that, if we apply the input sequence $v$ to the machine started in the state, we should observe output sequence $u$. We give a necessary and sufficient condition that a function $p(u \mid v)$ be realizable as much as input-output function. Finally, we show Heller's result is extended by our condition.


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Michael Arbib. "Realization of Stochastic Systems." Ann. Math. Statist. 38 (3) 927 - 933, June, 1967.


Published: June, 1967
First available in Project Euclid: 27 April 2007

zbMATH: 0147.36801
MathSciNet: MR225606
Digital Object Identifier: 10.1214/aoms/1177698889

Rights: Copyright © 1967 Institute of Mathematical Statistics

Vol.38 • No. 3 • June, 1967
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