Open Access
December, 1978 On Generators of Subordinate Semigroups
Henryk Gzyl
Ann. Probab. 6(6): 975-983 (December, 1978). DOI: 10.1214/aop/1176995387


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 $(X, \tau)$.


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Henryk Gzyl. "On Generators of Subordinate Semigroups." Ann. Probab. 6 (6) 975 - 983, December, 1978.


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

zbMATH: 0403.60067
MathSciNet: MR512414
Digital Object Identifier: 10.1214/aop/1176995387

Primary: 60J35

Keywords: additive functional , infinitesimal generator , semigroup , Standard process

Rights: Copyright © 1978 Institute of Mathematical Statistics

Vol.6 • No. 6 • December, 1978
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