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This article is cited in 7 scientific papers (total in 7 papers)
On the problem of stochastic integral representations of functionals of the Browning motion. II
S. Graversena, A. N. Shiryaevb, M. Yorc a University of Aarhus, Department of Mathematical Sciences
b Steklov Mathematical Institute, Russian Academy of Sciences
c Université Pierre & Marie Curie, Paris VI
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 $S(\omega)$ of Brownian motion $B=(B_t)_{t\ge 0}$ was stated. Functionals $\max_{t\le T}B_t$ and $\max_{t\le T_{-a}}B_t$, where $T_{-a}=\inf\{t: B_t=-a\}$, $a>0$, 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 $\max_{t\le g_T}B_t$, where (non-Markov time) $g_T=\sup\{0\le t\le T:B_t=0\}$ are given.
Keywords:
Brownian motion, Itô integral, max-functionals, stochastic integral representation.
Received: 05.12.2005
Citation:
S. Graversen, A. N. Shiryaev, M. Yor, “On the problem of stochastic integral representations of functionals of the Browning motion. II”, Teor. Veroyatnost. i Primenen., 51:1 (2006), 64–77; Theory Probab. Appl., 51:1 (2007), 65–77
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https://www.mathnet.ru/eng/tvp146https://doi.org/10.4213/tvp146 https://www.mathnet.ru/eng/tvp/v51/i1/p64
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