On the problem of stochastic integral representations of functionals of the brownian motion. II

S. Graversen, A. N. Shiryaev, M. Yor

    Research output: Contribution to journalArticlepeer-review

    Abstract

    In the first part of this paper [A. N. Shiryaev and M. Yor, Theory Probab. Appl., 48 (2004), pp. 304-313], a method of obtaining stochastic integral representations of functionals S(ω) of Brownian motion B = (B t)t≧0 was stated. Functionals maxt≦T Bt and maxt≦T-a Bt, where T-a = inf{t: Bt = -a}, a > 0, were considered as an illustration. In the present paper we state another derivation of representations for these functionals and two proofs of representation for functional max t≦gT Bt, where (non-Markov time) gT = sup{0 ≦ t ≦ T: Bt = 0} are given. © 2007 Society for Industrial and Applied Mathematics.
    Original languageEnglish
    Pages (from-to)65-77
    Number of pages12
    JournalTheory of Probability and Its Applications
    Volume51
    Issue number1
    DOIs
    Publication statusPublished - 2007

    Keywords

    • Brownian motion
    • Itô integral
    • Max-functionals
    • Stochastic integral representation

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