Geodesic
On distributions of integral functionals of diffusions stopped at inverse range time
Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 24, Tome 454 (2016), pp. 43-51 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice du chapitre de livre

In the paper we develop the methods for computations of distributions of integral functionals of diffusions stopped at inverse range time. We consider also the moment, which is the minimum of inverse range time and the exponentially distributed stopping time independent of the diffusion. An interesting example of the applications of these methods is considered. 
@article{ZNSL_2016_454_a1,
     author = {A. N. Borodin},
     title = {On distributions of integral functionals of diffusions stopped at inverse range time},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {43--51},
     year = {2016},
     volume = {454},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2016_454_a1/}
}
TY  - JOUR
AU  - A. N. Borodin
TI  - On distributions of integral functionals of diffusions stopped at inverse range time
JO  - Zapiski Nauchnykh Seminarov POMI
PY  - 2016
SP  - 43
EP  - 51
VL  - 454
UR  - http://geodesic.mathdoc.fr/item/ZNSL_2016_454_a1/
LA  - ru
ID  - ZNSL_2016_454_a1
ER  - 
%0 Journal Article
%A A. N. Borodin
%T On distributions of integral functionals of diffusions stopped at inverse range time
%J Zapiski Nauchnykh Seminarov POMI
%D 2016
%P 43-51
%V 454
%U http://geodesic.mathdoc.fr/item/ZNSL_2016_454_a1/
%G ru
%F ZNSL_2016_454_a1
A. N. Borodin. On distributions of integral functionals of diffusions stopped at inverse range time. Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 24, Tome 454 (2016), pp. 43-51. http://geodesic.mathdoc.fr/item/ZNSL_2016_454_a1/

[1] J. P. Imhof, “On the range of Brownian motion and its inverse process”, Ann. Probab., 13 (1985), 1–13 | DOI | MR

[2] P. Vallois, “Decomposition of the Brownian path via the range process”, Stoch. Proc. Appl., 55 (1995), 211–226 | DOI | MR | Zbl

[3] A. N. Borodin, “O raspredelenii funktsionalov ot brounovskogo dvizheniya, ostanovlennogo v moment, obratnyi k razmakhu”, Zap. nauchn. semin. POMI, 260, 1999, 50–72 | MR | Zbl

[4] A. N. Borodin, Sluchainye protsessy, Lan, Sankt-Peterburg, 2013

[5] A. N. Borodin, P. Salminen, Spravochnik po brounovskomu dvizheniyu. Fakty i formuly, Lan, Sankt-Peterburg, 2016