DOI

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 of 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.

Original languageEnglish
Pages (from-to)3597-3618
Number of pages22
JournalTransactions of the American Mathematical Society
Volume372
Issue number5
DOIs
StatePublished - 1 Sep 2019

    Research areas

  • Bessel function, Brownian motion, Inversion formula for Laplace transforms, Local time

    Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

ID: 46296238