IV: 15, 170-194, LNM 124 (1970)
MOKOBODZKI, Gabriel
Densité relative de deux potentiels comparables (
Potential theory)
The main problem considered here is the following: given a transient resolvent $(V_{\lambda})$ on a measurable space, a finite potential $Vg$, an excessive function $u$ dominated by $Vg$ in the strong sense (i.e., $Vg-u$ is excessive), show that $u=Vf$ for some $f\leq g$, and compute $f$ by some ``derivation'' procedure, like $\lim_{\lambda\rightarrow\infty} \lambda(I-\lambda V_{\lambda})\,u$
Comment: The main theorem and the technical tools of its proof have been landmarks in the potential theory of a resolvent, though in the case of the resolvent of a good Markov process there is a simple probabilistic proof of the main result. Another exposition can be found in
Séminaire Bourbaki, 422, November 1972. See also Chapter XII of Dellacherie-Meyer,
Probabilités et potentiel, containing new proofs due to Feyel
Keywords: Resolvents,
Strong ordering,
Lebesgue derivation theoremNature: Original
Retrieve article from Numdam
IV: 16, 195-207, LNM 124 (1970)
MOKOBODZKI, Gabriel
Quelques propriétés remarquables des opérateurs presque positifs (
Potential theory)
A sequel to the preceding paper
415. Almost positive operators are candidates to the role of derivation operators relative to a resolvent
Comment: Same as
415Keywords: Resolvents,
Strong ordering,
Lebesgue derivation theoremNature: Original Retrieve article from Numdam
V: 21, 211-212, LNM 191 (1971)
MEYER, Paul-André
Deux petits résultats de théorie du potentiel (
Potential theory)
Excessive functions are characterized by their domination property over potentials. The strong ordering relation between two functions is carried over to their réduites
Comment: See Dellacherie-Meyer
Probability and Potentials, Chapter XII, \S2
Keywords: Excessive functions,
Réduite,
Strong orderingNature: Original Retrieve article from Numdam
