Displaying similar documents to “Duality and the Martin compactification”

A new setting for potential theory. I

Kai Lai Chung, K. Murali Rao (1980)

Annales de l'institut Fourier

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We consider a transient Hunt process in which the potential density u satisfies the conditions: (a) for each x , u ( x , y ) - 1 is finite continuous in y ; (b) u ( x , y ) = + ∞ iff x = y . In earlier papers Chung established an equilibrium principle, and Rao obtained a Riesz of decomposition for excessive functions. We now begin a deeper study under these conditions, including the uniqueness of the decomposition and Hunt’s hypothesis (B).

Flux in axiomatic potential theory. II. Duality

Bertram Walsh (1969)

Annales de l'institut Fourier

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This is a continuation of an earlier paper [Inventiones Math., 8 (1969), 175-221]. It is assumed that a space W and a sheaf H over W are given, such that the pair ( W , H ) satisfies the Brelot axioms and also satisfies, locally, the additional hypotheses of the theory of adjoint sheaves. The following subjects are considered: 1) Extension of the adjoint-sheaf theory to the case where ( W , H ) does not admit a global potential (in particular, the case where W is compact). 2) Construction of a new fine...

Multiplicative functionals of dual processes

Ronald K. Getoor (1971)

Annales de l'institut Fourier

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Let X and X ^ be a pair of dual standard Markov processes. We associate to each exact multiplicative function ( M F ) , M of X a unique exact M F , M ^ of X ^ in a natural manner. Any M F , M is assumed to satisfy 0 ≤ M t ≤ 1 . The map M → M ^ is bijective and multiplicative in the sense that: ( M N ) ∧ = M ^ N ^ . This correspondence is studied in some detail and several important examples are discussed. These results are then applied to study additive functionals.