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JOURNALS // Zapiski Nauchnykh Seminarov POMI // Archive

Zap. Nauchn. Sem. POMI, 2021 Volume 501, Pages 36–51 (Mi znsl7076)

This article is cited in 2 papers

Distributions of functionals of local time of a skew Brownian motion with discontinuous drift

A. N. Borodin

St. Petersburg Department of Steklov Mathematical Institute of Russian Academy of Sciences

Abstract: 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.

Key words and phrases: Brownian motion with discontinuous drift, skew Brownian motion, local time.

UDC: 519.2

Received: 06.07.2021



© Steklov Math. Inst. of RAS, 2024