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
302Keywords: Recurrent sets,
Fine topologyNature: Original
Retrieve article from Numdam
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
201Keywords: Recurrent potential theory,
Invariant measuresNature: Original Retrieve article from Numdam
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 for``normal'' 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 theoryNature: Original Retrieve article from Numdam
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
Comment: To be asked
Keywords: Polar sets,
Semi-polar sets,
Excessive functionsNature: Original Retrieve article from Numdam
VI: 20, 202-214, LNM 258 (1972)
REVUZ, Daniel
Le principe semi-complet du maximum (
Potential theory)
The problem studied here (and not completely solved) consists in finding potential theoretic characterizations for the recurrent potential operators constructed in the basic paper of Neveu,
Ann. Inst. Fourier, 22-2, 1972. It is shown that these operators satisfy suitable maximum principles (as usual, slightly stronger in the discrete case than in the continuous case). The converse is delicate and some earlier work of Kondo (
Osaka J. Math.,
4, 1967) and Oshima (same journal,
6, 1969) is discussed in this new set-up
Comment: This topic is discussed again in Revuz' book
Markov Chains, North-Holland
Keywords: Recurrent potential theory,
Maximum principles,
Recurrent Markov chainsNature: Original Retrieve article from Numdam
