On the construction of Wiener integrals with respect to certain pseudo-Bessel processes
type: Item
instance of: scholarly article
title: On the construction of Wiener integrals with respect to certain pseudo-Bessel processes
zbMATH Open document ID: 1110.60055
author: Tadahisa Funaki
author: Yuu Hariya
author: Marc Yor
author: Francis Hirsch
published in: Stochastic Processes and their Applications
publication date: 2007-01-09T00:00:00Z
review text: Let \((B_t)\) be a standard real Brownian motion, \((R_t)\) be a \((B_t)\)-driven Bessel process, and \(B_t^{(s)}:=\frac{1}{\sqrt s} B_{st}\). In order to define stochastic integrals such as \(\int^1_0h(s)d [\sqrt sf(\frac{Bs}{\sqrt s})]\) or \(\int^1_0h(s)d[\sqrt sf(\frac{Rs}{\sqrt s})]\), for \(h\in L^2[0,1]\), the authors are led to consider the existence of integrals \(\int^1_0h(s)_xF[B^{(s)}]\frac {ds}{\sqrt s}\), where \(F\) is some Brownian functional. They find that this existence is in turn guaranteed by the finiteness of \(C^*_F:=\int^1_0|\mathbb{E} [F(B)_xF (B^{(s)})]|\frac{ds}{s}\). They study some sufficient conditions ensuring \(C^*_F<\infty\), and apply them in particular to the examples: \(F(B)= g(B_1)\) and \(F(B)=g(R_1)\).
reviewed by: Jacques Franchi
Mathematics Subject Classification ID: 60H05
Mathematics Subject Classification ID: 60J65
Mathematics Subject Classification ID: 60J60
zbMATH DE Number: 5083375
zbMATH Keywords: Itô's representation theorem
zbMATH Keywords: scaling property
zbMATH Keywords: Gebelein's inequality
zbMATH Keywords: Hermite and Laguerre series expansions
MaRDI profile type: Publication
full work available at URL: j.spa.2006.05.001
OpenAlex ID: W2068380815
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DOI: 10.1016/J.SPA.2006.05.001
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description: scientific article; zbMATH DE number 5083375