Some results about Markov processes on subsets of the state space
Cristina Gzyl · Advances in Applied Probability · 1976
Kingman [5] proved a formula that expresses the joint distribution of the processes where b is a regular point in the state space of a Hunt process. We give an extension of this formula, as well as several interesting facts related to it, for the case when Φ is any finely perfect subset of the state space. We also establish some connections between this result and results on last-exit decompositions.