Geodesic
On the Markov property of the occupation time for continuous-time inhomogeneous Markov chains
Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 20, Tome 420 (2013), pp. 23-49 Cet article a éte moissonné depuis la source Math-Net.Ru

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It is known that the occupation time random field for a homogeneous Markov chain is Markovian. One investigates the possibility of generalizing this result for inhomogeneous chains. Consider a process which is a homogeneous Markov chain with the transition probability density $Q_1$ up to time $T$ and with the density $Q_2$ after $T$ ($Q_1\ne Q_2$). It turns out that even in this simplest case the occupation time is not Markovian. 
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A. A. Vorotov. On the Markov property of the occupation time for continuous-time inhomogeneous Markov chains. Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 20, Tome 420 (2013), pp. 23-49. http://geodesic.mathdoc.fr/item/ZNSL_2013_420_a1/

[1] S. S. Vallander, “Vremena prebyvaniya dlya neodnorodnykh tsepei Markova s diskretnym vremenem”, Zap. nauchn. semin. LOMI, 177, 1989, 37–45 | MR | Zbl

[2] S. S. Vallander, “Vremena prebyvaniya dlya schetnykh tsepei Markova. I. Tsepi s diskretnym vremenem”, Zap. nauchn. semin. LOMI, 119, 1982, 39–61 | MR | Zbl

[3] S. S. Vallander, “Vremena prebyvaniya dlya schetnykh tsepei Markova. II. Tsepi s nepreryvnym vremenem”, Zap. nauchn. semin. LOMI, 130, 1983, 56–64 | MR

[4] S. S. Vallander, “Vremena prebyvaniya dlya schetnykh tsepei Markova. III. Tsepi na dereve s odnoi tochkoi vetvleniya”, Zap. nauchn. semin. LOMI, 142, 1985, 25–38 | MR | Zbl

[5] S. S. Vallander, “Vremena prebyvaniya dlya schetnykh tsepei Markova. IV. Tsepi na proizvolnom dereve”, Zap. nauchn. semin. LOMI, 158, 1987, 39–44 | Zbl

[6] S. S. Vallander, “Nekotorye svoistva vremen prebyvaniya i perekhodov dlya schetnykh tsepei Markova”, Tezisy dokladov Chetvertoi Mezhdunarodnoi Vilnyusskoi konferentsii po teorii veroyatnostei i matematicheskoi statistike, v. 1, Vilnyus, 1985, 116–118

[7] S. S. Vallander, “Polya prebyvaniya i perekhodov dlya schetnykh tsepei Markova”, Shestoi mezhdunarodnyi sipozium po teorii informatsii, Tezisy dokladov, ch. III, 1984, 64–66

[8] A. A. Vorotov, “Markovskoe svoistvo polya vremeni prebyvaniya dlya diskretnykh markovskikh protsessov”, Zap. nauchn. semin. POMI, 412, 2013, 88–108 | MR

[9] K. Ito, G. Makkin, Diffuzionnye protsessy i ikh traektorii, Mir, M., 1968