Mesures associées aux fonctionnelles additives de Markov. I

Abstract

With each additive functional of Markov processes we associate a measure and characterize, under duality hypotheses, those which correspond to <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="sigma"> <mml:semantics> <mml:mi>σ<!-- σ --></mml:mi> <mml:annotation encoding="application/x-tex">\sigma</mml:annotation> </mml:semantics> </mml:math> </inline-formula>-finite measures. This enables us to weaken the hypotheses of Meyer’s theorem on representation of potentials of measures as potentials of additive functional. We characterize also the measures which are associated with continuous additive functionals. This leads us to show that for each finite continuous additive functional of the process there exists a finite continuous additive functional of the dual process such that the corresponding time-changed processes are in duality. Similar results are also stated for subprocesses which generalize results by Hunt and Blumenthal and Getoor.

Locations

• Transactions of the American Mathematical Society - View - PDF