Geodesic
Distribution of functionals of Brownian motion with linear drift killed elastically at zero
Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 31, Tome 505 (2021), pp. 62-74 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice du chapitre de livre

Brownian motion with linear drift on the positive half-line killed elastically at zero is cosidered. We are interested in a result that allows us to calculate the distributions of the integral functionals with respect to the spatial variable of the local time of such process. The explicit form of the distribution of the supremum with respect to spatial variable of the local time is calculated for Brownian motion with linear drift reflected at zero. 
@article{ZNSL_2021_505_a3,
     author = {A. N. Borodin},
     title = {Distribution of functionals of {Brownian} motion with linear drift killed elastically at zero},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {62--74},
     year = {2021},
     volume = {505},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2021_505_a3/}
}
TY  - JOUR
AU  - A. N. Borodin
TI  - Distribution of functionals of Brownian motion with linear drift killed elastically at zero
JO  - Zapiski Nauchnykh Seminarov POMI
PY  - 2021
SP  - 62
EP  - 74
VL  - 505
UR  - http://geodesic.mathdoc.fr/item/ZNSL_2021_505_a3/
LA  - ru
ID  - ZNSL_2021_505_a3
ER  - 
%0 Journal Article
%A A. N. Borodin
%T Distribution of functionals of Brownian motion with linear drift killed elastically at zero
%J Zapiski Nauchnykh Seminarov POMI
%D 2021
%P 62-74
%V 505
%U http://geodesic.mathdoc.fr/item/ZNSL_2021_505_a3/
%G ru
%F ZNSL_2021_505_a3
A. N. Borodin. Distribution of functionals of Brownian motion with linear drift killed elastically at zero. Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 31, Tome 505 (2021), pp. 62-74. http://geodesic.mathdoc.fr/item/ZNSL_2021_505_a3/

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

[2] A. N. Borodin, P. Salminen, “On the local time process of a skew Brownian motion”, Trans. Amer. Math. Soc., 372:5 (2019), 3597–3618 | DOI | MR | Zbl

[3] A. N. Borodin, “Raspredeleniya funktsionalov ot lokalnogo vremeni brounovskogo dvizheniya s razryvnym snosom”, Zap. nauchn. semin. POMI, 495, 2020, 102–121

[4] A. N. Borodin, Sluchainye protsessy, Lan, Sankt-Peterburg, 2017

[5] F. B. Knight, “Random walks and a sojourn density process of Brownian motion”, Trans. Amer. Math. Soc., 109 (1963), 56–86 | DOI | MR | Zbl

[6] D. B. Ray, “Sojourn times of a diffusion process”, Ill. J. Math., 7 (1963), 615–630 | Zbl

[7] G. N. Kinkladze, “A note on the structure of processes the measure of which is absolutely continuous with respect to Wiener process modulus measure”, Stochastics, 8 (1982), 39–84 | DOI | MR

[8] A. N. Borodin, “Raspredeleniya funktsionalov ot skoshennogo brounovskogo dvizheniya s razryvnym snosom”, Zap. nauchn. semin. POMI, 50, 2021, 36–51

[9] M. Abramovits, I. Stigan, Spravochnik po spetsialnym funktsiyam, Nauka, M., 1979