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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



Random evolution processes with feedback

Author: Kyle Siegrist
Journal: Trans. Amer. Math. Soc. 265 (1981), 375-392
MSC: Primary 60J25
MathSciNet review: 610955
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Abstract: A general random evolution Markov process is constructed which switches back and forth at random among a given collection of Markov processes ("modes of evolution") defined on a common evolution state space and indexed by an evolution rule space. Feedback is incorporated by allowing the path of the evolution component to influence the changes in evolution rule. The semigroup of the random evolution process is studied and is used to compare the process with the operator random evolutions of Griego and Hersh. Using deterministic modes of evolution, we generalize the Markov processes constructed by Erickson and by Heath. We also study new random evolution processes constructed from Brownian motions and from regular step processes.

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Keywords: Markov process, random evolution, semigroup, infinitesimal operator, Brownian motion, regular step process
Article copyright: © Copyright 1981 American Mathematical Society