Geodesic
Markov property of the occupation time for countable Markov chains
Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 19, Tome 412 (2013), pp. 88-108

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The paper deals with the Markov property for the occupation time process for homogeneous Markov chain with continuous time and countable state space. The well-known result that the Markov property is valid for random walk on a tree is generalized on the case of random walk on arbitrary graph. 
@article{ZNSL_2013_412_a4,
     author = {A. A. Vorotov},
     title = {Markov property of the occupation time for countable {Markov} chains},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {88--108},
     publisher = {mathdoc},
     volume = {412},
     year = {2013},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2013_412_a4/}
}
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A. A. Vorotov. Markov property of the occupation time for countable Markov chains. Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 19, Tome 412 (2013), pp. 88-108. http://geodesic.mathdoc.fr/item/ZNSL_2013_412_a4/