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Bridges of Markov counting processes. Reciprocal classes and duality formulas. (English) Zbl 1328.60178
Summary: Processes sharing the same bridges are said to belong to the same reciprocal class. In this article, we analyze reciprocal classes of Markov counting processes by identifying their reciprocal invariant and we characterize them as the set of counting processes satisfying some duality formula.

MSC:
60J27 Continuous-time Markov processes on discrete state spaces
60H07 Stochastic calculus of variations and the Malliavin calculus
60G51 Processes with independent increments; Lévy processes
60G57 Random measures
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