Homogeneous potentials
On the construction of kernels
Transience and recurrence of Markov processes
Multiplicative functionals of dual processes
Let and be a pair of dual standard Markov processes. We associate to each exact multiplicative function , of a unique exact , of in a natural manner. Any , is assumed to satisfy . The map is bijective and multiplicative in the sense that: . This correspondence is studied in some detail and several important examples are discussed. These results are then applied to study additive functionals.
Some applications of quasi-boundedness for excessive measures
Some Random Time Dilations of a Markov Process.
The Ray space of a right process
Let be a process with state space satisfying (a somewhat relaxed version of) Meyer’s “hypothèses droites”. Then by introducing a new topology (called the Ray topology) on and a compactification of in the Ray topology one can regard as a Ray process. However, this construction depends on the choice of an arbitrary uniformity on and not just the topology of . We show that the Ray topology is independent of the choice of this uniformity. We then introduce a space (the Ray space) which...
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