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Abstract  The perturbation of the generator of a Borel right process by a signed measure is investigated, using probabilistic and analytic potential theoretical methods. We establish a Feynman-Kac formula associated with measures charging no polar set and belonging to an extended Kato class. A main tool of this approach is the validity of a Khas’minskii Lemma for Stieltjes exponentials of positive left continuous additive functionals. [ABSTRACT FROM AUTHOR]

Abstract  We present an analytic version of the following uniqueness problem for Markov processes: if two subprocesses of a given transient, Borel right process have the same excessive functions then they coincide. Our treatment is given in terms of subordinate sub-Markovian resolvents of kernels in the sense of P. A. Mayer and uses essentially the subordination operators introduced by G. Mokobodzki. [ABSTRACT FROM AUTHOR]

Abstract We answer to a question of P.J. Fitzsimmons and R.K. Getoor concerning the characterization of a strongly supermedian function by the property of being “universally” supermedian. Based on the Revuz correspondence we also prove (alternatively to the probabilistic approach of Fitzsimmons and Getoor) that the Radon–Nikodym derivative between the Revuz measures of a semiregular excessive kernel and the regular strongly supermedian kernel generating it, does not depend on the kernel. [ABSTRACT FROM AUTHOR]

Suppose that U is the resolvent of a Borel right process on a Lusin space X. If ξ is a U-excessive measure on X then we show by analytical methods that for every U-excessive measure η with η≪ξ the Radon–Nikodym derivative dη/dξ possesses a finely continuous version. (Fitzsimmons and Fitzsimmons and Getoor gave a probabilistic approach for this result.) We extend essentially a technique initiated by Mokobodzki and deepened by Feyel. The result allows us to establish a Revuz type formula involving the fine versions, and to study the Revuz correspondence between the σ-finite measures charging no set that is both ξ-polar and ρ-negligible (ρ○U being the potential component of ξ) and the strongly supermedian kernels on X. This is an analytic version of a result of Azéma, Fitzsimmons and Dellacherie, Maisonneuve and Meyer, in terms of additive functionals or homogeneous random measures. Finally we give an application to the context of the semi-Dirichlet forms, covering a recent result of Fitzsimmons. [ABSTRACT FROM AUTHOR]