Geodesic
On the limit distribution function for meanings of a diffusion semi-Markov process on interval with unattainable boundaries
Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 31, Tome 505 (2021), pp. 312-323 
B. P. Harlamov. On the limit distribution function for meanings of a diffusion semi-Markov process on interval with unattainable boundaries. Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 31, Tome 505 (2021), pp. 312-323. http://geodesic.mathdoc.fr/item/ZNSL_2021_505_a17/
@article{ZNSL_2021_505_a17,
     author = {B. P. Harlamov},
     title = {On the limit distribution function for meanings of a diffusion {semi-Markov} process on interval with unattainable boundaries},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {312--323},
     year = {2021},
     volume = {505},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2021_505_a17/}
}
TY  - JOUR
AU  - B. P. Harlamov
TI  - On the limit distribution function for meanings of a diffusion semi-Markov process on interval with unattainable boundaries
JO  - Zapiski Nauchnykh Seminarov POMI
PY  - 2021
SP  - 312
EP  - 323
VL  - 505
UR  - http://geodesic.mathdoc.fr/item/ZNSL_2021_505_a17/
LA  - ru
ID  - ZNSL_2021_505_a17
ER  - 
%0 Journal Article
%A B. P. Harlamov
%T On the limit distribution function for meanings of a diffusion semi-Markov process on interval with unattainable boundaries
%J Zapiski Nauchnykh Seminarov POMI
%D 2021
%P 312-323
%V 505
%U http://geodesic.mathdoc.fr/item/ZNSL_2021_505_a17/
%G ru
%F ZNSL_2021_505_a17

Voir la notice du chapitre de livre provenant de la source Math-Net.Ru

A diffusion semi-Markov process on a finite interval with unattainable boundaries is considered. It is supposed that unattainable property is not be connected with process stop in the interval. A limit theorem for alternating renewal processes is applied for to derive the limit distribution function of the diffusion process.

[1] I. I. Gikhman, A. V. Skorokhod, Teoriya sluchainykh protsessov, v. 2, Nauka, M., 1973

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

[3] E. B. Dynkin, Markovskie protsessy, Fizmatgiz, M., 1963

[4] B. P. Kharlamov, “Finalnoe raspredelenie diffuzionnogo protsessa s ostanovkoi”, Zap. nauchn. semin. POMI, 431, 2014, 209–241

[5] B. P. Kharlamov, “O nedostizhimoi granitse intervala znachenii diffuzionnogo protsessa: polumarkovskii podkhod”, Zap. nauchn. semin. POMI, 466, 2017, 313–330

[6] D. Koks, V. Smit, Teoriya vosstanovleniya, Sovetskoe radio, M., 1967

[7] A. N. Shiryaev, Veroyatnost, Nauka, M., 1980

[8] E. Kamke, Spravochnik po obyknovennym differentsialnym uravneniyam, Nauka, M., 1971