Geodesic
Occupation times for countable Markov chains.~IV. Chains on a general tree
Zapiski Nauchnykh Seminarov POMI, Problems of the theory of probability distributions. Part X, Tome 158 (1987), pp. 39-44

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The results of the author's preceding paper are carried over to a larger class of Markov chains. The Markov property of the dwelling time field is proved for chains with continuous time. 
@article{ZNSL_1987_158_a3,
     author = {S. S. Vallander},
     title = {Occupation times for countable {Markov} {chains.~IV.} {Chains} on a general tree},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {39--44},
     publisher = {mathdoc},
     volume = {158},
     year = {1987},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1987_158_a3/}
}
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S. S. Vallander. Occupation times for countable Markov chains.~IV. Chains on a general tree. Zapiski Nauchnykh Seminarov POMI, Problems of the theory of probability distributions. Part X, Tome 158 (1987), pp. 39-44. http://geodesic.mathdoc.fr/item/ZNSL_1987_158_a3/