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Wiener integrals for centered powers of Bessel processes, I
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- Funaki, Tadahisa
- Graduate School of Mathematical Sciences, The University of Tokyo
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- Hariya, Yuu
- Departement de Mathematiques, Institut Elie Cartan
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- Yor, Marc
- Laboratoire de Probabilites et Modeles Aleatoires, Universite Pierre et Marie Curie
Description
The stochastic integrals of Wiener’s type may be constructed relatively to the centered $ delta $-dimensional Bessel processes (BES($ delta $)-processes in short) and their variants based on two different approaches. One approach, developed in [3], is via the Brascamp-Lieb inequality which works especially well for the BES($ delta $)-processes, BES($ delta $)-bridges with $ delta geq 3 $ or for the Brownian meander. The other approach, which is the subject of the present paper, goes via Hardy’s $ L^2 $ inequality which is effective for general BES($ delta $)-processes and their powers. We shall also discuss an interplay of these two methods.
Journal
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- MHF Preprint Series
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MHF Preprint Series MHF2005-22 2005-05-19
Faculty of Mathematics, Kyushu University
