The Annals of Probability

On Generators of Subordinate Semigroups

Henryk Gzyl

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Abstract

Let $X$ be a standard Markov process with semigroup $(P_t)$. We show how to compute the infinitesimal generators (weak and strong) of the semigroup $Q_tf(x) = E^x\{m_tf(X_t)\}$ with $m_t = \exp(-\tau_t)$ and $\tau_t$ a right continuous, increasing strong additive functional; the computation is in terms of the infinitesimal operators of $(P_t)$ and the Levy system of the joint process $(X, \tau)$.

Article information

Source
Ann. Probab., Volume 6, Number 6 (1978), 975-983.

Dates
First available in Project Euclid: 19 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aop/1176995387

Digital Object Identifier
doi:10.1214/aop/1176995387

Mathematical Reviews number (MathSciNet)
MR512414

Zentralblatt MATH identifier
0403.60067

JSTOR
links.jstor.org

Subjects
Primary: 60J35: Transition functions, generators and resolvents [See also 47D03, 47D07]

Keywords
Standard process additive functional semigroup infinitesimal generator

Citation

Gzyl, Henryk. On Generators of Subordinate Semigroups. Ann. Probab. 6 (1978), no. 6, 975--983. doi:10.1214/aop/1176995387. https://projecteuclid.org/euclid.aop/1176995387


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