Open Access
October, 1989 A Sufficient Condition for Two Markov Semigroups to Commute
A. L. Bequillard
Ann. Probab. 17(4): 1478-1482 (October, 1989). DOI: 10.1214/aop/1176991168


Let $\{P^{(k)}_t, t \geq 0\}, k = 1, 2$, be two Markov semigroups on $\hat{C}(E)$, the space of continuous functions on a separable, locally compact metric space $E$ which tend to zero at infinity. In this article, we derive a sufficient condition for the two semigroups to commute, in the sense that for each $s \geq 0, t \geq 0$ and each $f \in \hat{C}(E), P^{(1)}_s P^{(2)}_t f = P^{(2)}_t P^{(1)}_s f$.


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A. L. Bequillard. "A Sufficient Condition for Two Markov Semigroups to Commute." Ann. Probab. 17 (4) 1478 - 1482, October, 1989.


Published: October, 1989
First available in Project Euclid: 19 April 2007

zbMATH: 0686.60074
MathSciNet: MR1048940
Digital Object Identifier: 10.1214/aop/1176991168

Keywords: 60J , Markov process , Martingale problem , semigroup

Rights: Copyright © 1989 Institute of Mathematical Statistics

Vol.17 • No. 4 • October, 1989
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