Geodesic
On the problem of stochastic integral representations of functionals of the Browning motion. II
Teoriâ veroâtnostej i ee primeneniâ, Tome 51 (2006) no. 1, pp. 64-77 Cet article a éte moissonné depuis la source Math-Net.Ru

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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, max-functionals, stochastic integral representation.
Mots-clés : Itô integral 
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S. Graversen; A. N. Shiryaev; M. Yor. On the problem of stochastic integral representations of functionals of the Browning motion. II. Teoriâ veroâtnostej i ee primeneniâ, Tome 51 (2006) no. 1, pp. 64-77. http://geodesic.mathdoc.fr/item/TVP_2006_51_1_a4/

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