Geodesic
Distribution of functionals of local time of Brownian motion with discontinuous drift
Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 29, Tome 495 (2020), pp. 102-120 
A. N. Borodin. Distribution of functionals of local time of Brownian motion with discontinuous drift. Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 29, Tome 495 (2020), pp. 102-120. http://geodesic.mathdoc.fr/item/ZNSL_2020_495_a5/
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     author = {A. N. Borodin},
     title = {Distribution of functionals of local time of {Brownian} motion with discontinuous drift},
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     year = {2020},
     volume = {495},
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     url = {http://geodesic.mathdoc.fr/item/ZNSL_2020_495_a5/}
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Voir la notice du chapitre de livre provenant de la source Math-Net.Ru

Diffusion with piecewise constant drift and the diffusion coefficient 1 is considered. We call this process the Brownian motion with discontinuous drift. With equal constants this diffusion includes Brownian motion with linear drift, and with opposite sign constants it turns into Brownian motion with alternating drift. We are interested in the result that allows us to calculate the distributions of the integral functionals with respect to the spatial variable of the local time of Brownian motion with discontinuous drift. The explicit form of the distribution of the supremum with respect to spatial variable of the local time of Brownian motion with discontinuous drift is calculated.

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

[2] 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

[3] A. N. Borodin, Stochastic Processes, Birkhäuser, Cham, Switzerland, 2017 | Zbl

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

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

[6] 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

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

[8] G. Beitmen, A. Erdeii, Tablitsy integralnykh preobrazovanii, v. 1, Nauka, M., 1969