Duality for a class of continuous-time reversible Markov models

Using a conditional probability structure we build transition probabilities that drive appealing classes of reversible Markov processes. The mechanism used in such a construction allows to find a dual Markov process. This kind of duality is then used to compute the predictor operator of one process via its dual. In particular, we identify the dual of some non-conjugate models, namely the M/M/infinity queue model and a simple birth, death and immigration process. Such duals ensure that the computation of the predictor operators can be done via finite sums.