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.
"Bridges of Markov counting processes. Reciprocal classes and duality formulas." Electron. Commun. Probab. 20 1 - 12, 2015. https://doi.org/10.1214/ECP.v20-3697