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: 24, 251-269, LNM 191 (1971)
MEYER, Paul-André
Solutions de l'équation de Poisson dans le cas récurrent (
Potential theory,
Markov processes)
The problem is to solve the Poisson equation for measures, $\mu-\mu P=\theta$ for given $\theta$, in the case of a recurrent transition kernel $P$. Here a ``filling scheme'' technique is used
Comment: The paper was motivated by Métivier (
Ann. Math. Stat.,
40, 1969) and is completely superseded by one of Revuz (
Ann. Inst. Fourier, 21, 1971)
Keywords: Recurrent potential theory,
Filling scheme,
Harris recurrence,
Poisson equationNature: 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
