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February, 1975 Functionals of Markov Processes and Superprocesses
Talma Leviatan
Ann. Probab. 3(1): 41-48 (February, 1975). DOI: 10.1214/aop/1176996446


It is well known that a contraction multiplicative functional $\alpha_t, t \geqq 0$ on some Markov process with transition $P_t, t \geqq 0$, yields another Markov process whose semigroup $Q_t(x, A) = E_x(\alpha_t, X_t \in A)$ is subordinate to $P_t, t \geqq 0$. The second process results from the original one by adding a killing operation at a rate of $-d\alpha_t/\alpha_t$. This paper deals with expansion multiplicative functionals (satisfying $\alpha_t \geqq 1$ and $E_x(\alpha_t) < \infty)$. It is proved that such functionals yield a Markov process with creation and annihilation of mass. Relations to the original process are established. Finally the results are generalized to, so-called, conditionally monotone functionals.


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Talma Leviatan. "Functionals of Markov Processes and Superprocesses." Ann. Probab. 3 (1) 41 - 48, February, 1975.


Published: February, 1975
First available in Project Euclid: 19 April 2007

zbMATH: 0302.60043
MathSciNet: MR400411
Digital Object Identifier: 10.1214/aop/1176996446

Keywords: 6062 , 6067 , dominating semigroup , Expansions multiplicative functionals , Markov processes with creation and annihilation

Rights: Copyright © 1975 Institute of Mathematical Statistics


Vol.3 • No. 1 • February, 1975
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