Distributions of functionals of local time of a skew Brownian motion with discontinuous drift
Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 30, Tome 501 (2021), pp. 36-51 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice du chapitre de livre

A skew Brownian motion with piecewise constant drift is considered. With equal constants this diffusion includes a skew Brownian motion with linear drift and with opposite sign constants it turns into a skew Brownian motion with alternating drift. 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 a skew Brownian motion with discontinuous drift.
@article{ZNSL_2021_501_a3,
     author = {A. N. Borodin},
     title = {Distributions of functionals of local time of a skew {Brownian} motion with discontinuous drift},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {36--51},
     year = {2021},
     volume = {501},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2021_501_a3/}
}
TY  - JOUR
AU  - A. N. Borodin
TI  - Distributions of functionals of local time of a skew Brownian motion with discontinuous drift
JO  - Zapiski Nauchnykh Seminarov POMI
PY  - 2021
SP  - 36
EP  - 51
VL  - 501
UR  - http://geodesic.mathdoc.fr/item/ZNSL_2021_501_a3/
LA  - ru
ID  - ZNSL_2021_501_a3
ER  - 
%0 Journal Article
%A A. N. Borodin
%T Distributions of functionals of local time of a skew Brownian motion with discontinuous drift
%J Zapiski Nauchnykh Seminarov POMI
%D 2021
%P 36-51
%V 501
%U http://geodesic.mathdoc.fr/item/ZNSL_2021_501_a3/
%G ru
%F ZNSL_2021_501_a3
A. N. Borodin. Distributions of functionals of local time of a skew Brownian motion with discontinuous drift. Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 30, Tome 501 (2021), pp. 36-51. http://geodesic.mathdoc.fr/item/ZNSL_2021_501_a3/

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

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

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

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

[5] A. N. Borodin, “Raspredeleniya funktsionalov ot lokalnogo vremeni brounovskogo dvizheniya s razryvnym snosom”, Zap. nauchn. semin. POMI, 496, 2020, 102–121

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

[7] S.-E. Graversen, A. N. Shiryaev, “An extension of P. Lévy's distributional properties to the case of a Brownian motion”, Bernoulli, 6 (2000), 615–620 | DOI | MR | Zbl

[8] 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