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

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

Item Type: Article
Uncontrolled Keywords: Brownian motion; Itô integral; max-functionals; stochastic integral representation
Subjects: MSC 2010, the AMS's Mathematics Subject Classification > 60 Probability theory and stochastic processes
Depositing User: Ms Lucy van Russelt
Date Deposited: 19 Nov 2007
Last Modified: 20 Oct 2017 14:12
URI: http://eprints.maths.manchester.ac.uk/id/eprint/911

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