On the local time process of a skew Brownian motion

Andrei Borodin, Paavo Salminen

    Tutkimustuotos: LehtiartikkeliArtikkeliTieteellinenvertaisarvioitu

    5 Sitaatiot (Scopus)
    15 Lataukset (Pure)

    Abstrakti

    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.

    AlkuperäiskieliEi tiedossa
    Sivut3597–3618
    JulkaisuTransactions of the American Mathematical Society
    Vuosikerta372
    Numero5
    DOI - pysyväislinkit
    TilaJulkaistu - 2019
    OKM-julkaisutyyppiA1 Julkaistu artikkeli, soviteltu

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