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February, 1978 A Generalization of Markov Processes
Abel Klein
Ann. Probab. 6(1): 128-132 (February, 1978). DOI: 10.1214/aop/1176995616


Osterwalder-Schrader (OS) positive symmetric stationary stochastic processes are discussed. A natural construction is given for the associated positive semigroup structure. Conversely, OS-positive symmetric stationary stochastic processes are constructed from positive semigroup structures. OS-positive processes are seen to be the natural generalization of Markov processes, positive semigroup structures being the natural generalization of positivity preserving semigroups. The inheritability of OS-positivity is discussed.


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Abel Klein. "A Generalization of Markov Processes." Ann. Probab. 6 (1) 128 - 132, February, 1978.


Published: February, 1978
First available in Project Euclid: 19 April 2007

zbMATH: 0374.60112
MathSciNet: MR518418
Digital Object Identifier: 10.1214/aop/1176995616

Primary: 60J99

Keywords: Markov processes , OS-positive symmetric stationary stochastic processes

Rights: Copyright © 1978 Institute of Mathematical Statistics

Vol.6 • No. 1 • February, 1978
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