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5 matches found
II: 01, 1-21, LNM 51 (1968)
AZÉMA, Jacques; DUFLO, Marie; REVUZ, Daniel
Classes récurrentes d'un processus de Markov (Markov processes)
This is an improved version of a paper by the same authors (Ann. Inst. H. Poincaré, 2, 1966). Its aim is a theory of recurrence in continuous time (for a Hunt process). The main point is to use the finely open sets instead of the ordinary ones to define recurrence
Comment: The subject is further investigated by the same authors in 302
Keywords: Recurrent sets, Fine topology
Nature: Original
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III: 02, 24-33, LNM 88 (1969)
AZÉMA, Jacques; DUFLO, Marie; REVUZ, Daniel
Mesure invariante des processus de Markov récurrents (Markov processes)
A condition similar to the Harris recurrence condition is studied in continuous time. It is shown that it implies the existence (up to a constant factor) of a unique $\sigma$-finite excessive measure, which is invariant. The invariant measure for a time-changed process is described
Comment: This is related to several papers by the same authors on recurrent Markov processes, and in particular to 201
Keywords: Recurrent potential theory, Invariant measures
Nature: Original
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IV: 17, 208-215, LNM 124 (1970)
REVUZ, Daniel
Application d'un théorème de Mokobodzki aux opérateurs potentiels dans le cas récurrent (Potential theory, Markov processes)
Mokododzki's theorem asserts that if the kernels of a resolvent are strong Feller, i.e., map bounded functions into continuous functions, then they must satisfy a norm continuity property (see 210). This is used to show the existence fornormal'' recurrent processes of a nice potential operator, defined for suitable functions of zero integral with respect to the invariant measure
Comment: For additional work of Revuz on recurrence, see Ann. Inst. Fourier, 21, 1971
Keywords: Recurrent potential theory
Nature: Original
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V: 26, 275-277, LNM 191 (1971)
REVUZ, Daniel
Remarque sur les potentiels de mesure (Markov processes, Potential theory)
The standard proof of the equivalence between semi-polar sets being polar and a very precise domination principle (Blumenthal-Getoor, Markov Processes and Potential Theory, 1968) uses the assumption that excessive functions are lower semicontinuous. This assumption is weakened