Geodesic
Diffusion processes with delay on ends of a segment
Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 12, Tome 351 (2007), pp. 284-297 
B. P. Harlamov. Diffusion processes with delay on ends of a segment. Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 12, Tome 351 (2007), pp. 284-297. http://geodesic.mathdoc.fr/item/ZNSL_2007_351_a16/
@article{ZNSL_2007_351_a16,
     author = {B. P. Harlamov},
     title = {Diffusion processes with delay on ends of a segment},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {284--297},
     year = {2007},
     volume = {351},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2007_351_a16/}
}
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Voir la notice du chapitre de livre provenant de la source Math-Net.Ru

A continuous semi-Markov process with a segment as a range of values is considered. This process is being transformed into a diffusion process inside the segment, i.e., up to the first hitting time on the boundary of the segment and any time leaving the boundary. Some conditions in terms of a semi-Markov transition generating function on the boundary for such a process to exist are derived. A method of imbedded alternating renewal processes is applied to find a stationary distribution of the process.

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[2] V. M. Shurenkov, Ergodicheskie protsessy Markova, Nauka, M., 1989

[3] B. P. Kharlamov, Nepreryvnye polumarkovskie protsessy, Nauka, SPb, 2001