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
VI: 15, 164-167, LNM 258 (1972)
MEYER, Paul-André
Une note sur le théorème du balayage de Hunt (
Markov processes,
Potential theory)
The theorem involved is the characterization of the réduite $P_A u$ of an excessive function $u$ on a set $A$ as equal (except on a well-defined semipolar set) to the infimum of the excessive functions that dominate $u$ on $A$. This theorem is slightly improved under the absolute continuity hypothesis. The proof rests on the following property of the fine topology: every (nearly Borel) finely closed set is contained in a fine $G_\delta$ which differs from it by a polar set
Keywords: Réduite,
Fine topology,
Absolute continuity hypothesisNature: Original Retrieve article from Numdam
