On the local time process of a skew Brownian motion

A1 Journal article (refereed)


Internal Authors/Editors


Publication Details

List of Authors: Andrei Borodin, Paavo Salminen
Publication year: 2019
Journal: Transactions of the American Mathematical Society
Volume number: 372
Issue number: 5
Start page: 3597
End page: 3618


Abstract

We derive a Ray-Knight type theorem for the local time process (in the space variable) of a skew Brownian motion up to an independent exponential time. It is known that the local time seen as a density of the occupation measure and taken with respect to the Lebesgue measure has a discontinuity at the skew point (in our case at zero), but the local time taken with respect to the speed measure is continuous. In this paper we discuss this discrepancy by characterizing the dynamics of the local time process in both these cases. The Ray-Knight type theorem is applied to study integral functionals of the local time process of the skew Brownian motion. In particular, we determine the distribution of the maximum of the local time process up to a fixed time, which can be seen as the main new result of the paper.


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