II: 11, 175-199, LNM 51 (1968)
MEYER, Paul-André
Compactifications associées à une résolvante (
Potential theory)
Let $E$ be a locally compact space, $(U_p)$ be a submarkovian resolvent, with a potential kernel $U=U_0$ which maps $C_k$ (the continuous functions with compact support) into continuous bounded functions. Let $F$ be a compact space containing $E$ as a dense subset, but inducing possibly a coarser topology. It is assumed that all potentials $Uf$ with $f\in C_k$ extend to continuous functions on $F$, and that points of $F$ are separated by continuous functions on $F$ whose restriction to $E$ is supermedian. Then it is shown how to extend the resolvent to $F$ and imitate the construction of a Ray semigroup and a strong Markov process. This was an attempt to compactify the space using only supermedian functions, not $p$-supermedian for all $p>0$. An application to Markov chains is given
Comment: This method of compactification suggested by Chung's boundary theory for Markov chains (similarly Doob,
Trans. Amer. Math. Soc.,
149, 1970) never superseded the standard Ray-Knight approach
Keywords: Resolvents,
Ray compactification,
Martin boundary,
Boundary theoryNature: Original
Retrieve article from Numdam
V: 19, 196-208, LNM 191 (1971)
MEYER, Paul-André
Représentation intégrale des fonctions excessives. Résultats de Mokobodzki (
Markov processes,
Potential theory)
Main result: the convex cone of excessive functions for a resolvent which satisfies the absolute continuity hypothesis is the union of convex compact metrizable ``hats''\ in a suitable topology, and therefore has the integral representation property. The original proof of Mokobodzki, self-contained and unpublished, is given here
Comment: See Mokobodzki's work on cones of potentials,
Séminaire Bourbaki, May 1970
Keywords: Minimal excessive functions,
Martin boundary,
Integral representationsNature: Exposition Retrieve article from Numdam
IX: 13, 305-317, LNM 465 (1975)
FÖLLMER, Hans
Phase transition and Martin boundary (
Miscellanea)
To be completed
Comment: To be completed
Keywords: Random fields,
Martin boundaryNature: Original Retrieve article from Numdam
