# On the problem of stochastic integral representations of functions of the Brownian motion II

Graversen, S. and Shiryaev, A. N. and Yor, M. (2007) On the problem of stochastic integral representations of functions of the Brownian motion II. Theory of Probability and its Applications, 51 (1). pp. 65-77. ISSN 1095-7219

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 $B=(B_t)_{t\ge0}$ 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.