Geodesic
On Markov diffusion processes with delayed reflection from interval's boundary
Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 15, Tome 368 (2009), pp. 243-267 
B. P. Harlamov. On Markov diffusion processes with delayed reflection from interval's boundary. Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 15, Tome 368 (2009), pp. 243-267. http://geodesic.mathdoc.fr/item/ZNSL_2009_368_a17/
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     author = {B. P. Harlamov},
     title = {On {Markov} diffusion processes with delayed reflection from interval's boundary},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {243--267},
     year = {2009},
     volume = {368},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2009_368_a17/}
}
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Voir la notice du chapitre de livre provenant de la source Math-Net.Ru

A continuous semi-Markov process taking values in a closed interval is considered. This process coincides with a Markov diffusion process inside the interval. Thus violation of the Markov property is possible only at extreme points of the interval. A sufficient condition for a semi-Markov process to be Markov is proved. It is proved that besides of Markov processes with instantaneous reflection from boundaries of the interval there exists a class of Markov processes with delayed reflection from them. Such a process has a positive average measure of time for its trajectory to be on the boundaries. Thus the other proof of the similar result of Gihman and Skorokhod (1968) is obtained. Bibl. – 5 titles.

[1] R. M. Blumenthal, R. K. Getoor, Markov processes and potential theory, Academic Press, New York, 1968 | MR

[2] I. I. Gikhman, A. V. Skorokhod, Stokhasticheskie differentsialnye uravneniya, Naukova dumka, Kiev, 1968 | MR | Zbl

[3] B. P. Kharlamov, “Kriterii markovosti nepreryvnykh polumarkovskikh protsessov”, Teor. veroyatn. i ee primen., 25:3 (1980), 535–548 | MR | Zbl

[4] B. P. Kharlamov, Nepreryvnye polumarkovskie protsessy, Nauka, SPb, 2001 | MR | Zbl

[5] B. P. Kharlamov, “Diffuzionnyi protsess s zaderzhkoi na krayakh otrezka”, Zap. nauchn. semin. POMI, 351, 2007, 284–297 | MR