Diffusion with piecewise constant drift and diffusion coefficient 1 is considered. Such a process is called the Brownian motion with discontinuous drift. At equal constants, this diffusion includes a Brownian motion with linear drift and at constants with opposite sign, it turns into a Brownian motion with variable drift. The goal of the paper is to get a result that allows 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.
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Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 495, 2020, pp. 102–120.
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Borodin, A.N. Distributions of Functionals of the Local Time of Brownian Motion with Discontinuous Drift. J Math Sci 268, 599–611 (2022). https://doi.org/10.1007/s10958-022-06230-y
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DOI: https://doi.org/10.1007/s10958-022-06230-y