On the local time process of a skew Brownian motion

D4 Publicerad utvecklings- eller forskningsrapport eller studie


Interna författare/redaktörer


Publikationens författare: Andrei Borodin, Paavo Salminen
Förläggare: arXiv
Publiceringsår: 2018


Abstrakt

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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Senast uppdaterad 2019-15-12 vid 03:34