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Multiplicative functionals of dual processes

Ronald K. Getoor — 1971

Annales de l'institut Fourier

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.

The Ray space of a right process

Ronald K. GetoorMichael J. Sharpe — 1975

Annales de l'institut Fourier

Let X be a process with state space E satisfying (a somewhat relaxed version of) Meyer’s “hypothèses droites”. Then by introducing a new topology (called the Ray topology) on E and a compactification F of E in the Ray topology one can regard X as a Ray process. However, this construction depends on the choice of an arbitrary uniformity on E and not just the topology of E . We show that the Ray topology is independent of the choice of this uniformity. We then introduce a space R (the Ray space) which...

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