Displaying similar documents to “Riesz representation and duality of Markov processes”

Duality and the Martin compactification

John C. Taylor (1972)

Annales de l'institut Fourier

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Let ℋ be a Bauer sheaf that admits a Green function. Then there exists a diffusion process corresponding to the sheaf whose resolvent possesses a Hunt-Kunita-Watanabe dual resolvent that comes from a diffusion process. If ℋ is a Brelot sheaf which possesses an adjoint sheaf ℋ * the dual process corresponds to ℋ * . The Martin compactification defined by a Brelot sheaf ℋ that admits a Green function coincides with a Kunita-Watanabe compactification defined by the dual resolvent. ...

Infinitely divisible processes and their potential theory. I

Sidney C. Port, Charles J. Stone (1971)

Annales de l'institut Fourier

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We show that associated with every i.d. (infinitely divisible) process on a locally compact, non-compact 2nd countable Abelian group is a corresponding potential theory that yields definitive results on the behavior of the process in both space and time. Our results are general, no density or other smoothness assumptions are made on the process. In this first part of two part work we have four main goals. (1) To lay the probabilistic foundation of such processes. This mainly...