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
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