The Annals of Probability

Functionals of Markov Processes and Superprocesses

Talma Leviatan

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Abstract

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.

Article information

Source
Ann. Probab., Volume 3, Number 1 (1975), 41-48.

Dates
First available in Project Euclid: 19 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aop/1176996446

Digital Object Identifier
doi:10.1214/aop/1176996446

Mathematical Reviews number (MathSciNet)
MR400411

Zentralblatt MATH identifier
0302.60043

JSTOR
links.jstor.org

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

Citation

Leviatan, Talma. Functionals of Markov Processes and Superprocesses. Ann. Probab. 3 (1975), no. 1, 41--48. doi:10.1214/aop/1176996446. https://projecteuclid.org/euclid.aop/1176996446


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