Geodesic
Final distribution of a diffusion process with a final stop
Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 21, Tome 431 (2014), pp. 209-241 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice du chapitre de livre

One-dimensional diffusion process is considered. A characteristic operator of this process is assumed to be a linear differential operator of the second order with a negative coefficient in the operator's member without derivative. Such an operator determines a measure of a Markov diffusion process with a break (the first interpretation), and also that of a semi-Markov diffusion process with a final stop (the second interpretation). Under the second interpretation the existence of a limit on infinity of the process (the final point) is characterized. This limit exists on any interval almost sure with respect to a conditional measure, generated by condition that the process never leaves this interval. A distribution of the final point expressed in terms of two fundamental solutions of the corresponding ordinary differential equation, and also that of the final stop beginning instant are derived. A homogeneous process is considered as an example. 
@article{ZNSL_2014_431_a13,
     author = {B. P. Harlamov},
     title = {Final distribution of a~diffusion process with a~final stop},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {209--241},
     year = {2014},
     volume = {431},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2014_431_a13/}
}
TY  - JOUR
AU  - B. P. Harlamov
TI  - Final distribution of a diffusion process with a final stop
JO  - Zapiski Nauchnykh Seminarov POMI
PY  - 2014
SP  - 209
EP  - 241
VL  - 431
UR  - http://geodesic.mathdoc.fr/item/ZNSL_2014_431_a13/
LA  - ru
ID  - ZNSL_2014_431_a13
ER  - 
%0 Journal Article
%A B. P. Harlamov
%T Final distribution of a diffusion process with a final stop
%J Zapiski Nauchnykh Seminarov POMI
%D 2014
%P 209-241
%V 431
%U http://geodesic.mathdoc.fr/item/ZNSL_2014_431_a13/
%G ru
%F ZNSL_2014_431_a13
B. P. Harlamov. Final distribution of a diffusion process with a final stop. Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 21, Tome 431 (2014), pp. 209-241. http://geodesic.mathdoc.fr/item/ZNSL_2014_431_a13/

[1] A. Borodin, P. Salminen, Spravochnik po brounovskomu dvizheniyu, Lan, SPb., 2000

[2] E. B. Dynkin, Markovskie protsessy, FM, M., 1963 | MR

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

[6] B. P. Kharlamov, “O tochkakh zaderzhki i asimmetrii odnomernogo polumarkovskogo diffuzionnogo protsessa”, Zap. nauchn. semin. POMI, 384, 2010, 291–309 | MR