TY - JOUR

T1 - Integration by parts formulae for Wiener measures on a path space between two curves

AU - Funaki, Tadahisa

AU - Ishitani, Kensuke

N1 - Funding Information:
The authors thank Dr. Steve Bagley for providing support and assistance with confocal microscopy and Dr. Chris Ward for critical analysis of the manuscript. This project was supported by funds from the Association for International Cancer Research and the Cancer Research Campaign.

PY - 2007/3

Y1 - 2007/3

N2 - This paper is concerned with the integration by parts formulae for the pinned or the standard Wiener measures restricted on a space of paths staying between two curves. The boundary measures, concentrated on the set of paths touching one of the curves once, are specified. Our approach is based on the polygonal approximations. In particular, to establish the convergence of boundary terms, a uniform estimate is derived by means of comparison argument for a sequence of random walks conditioned to stay between two polygons. Applying the Brascamp-Lieb inequality, the stochastic integrals of Wiener type are constructed relative to the three-dimensional Bessel bridge or the Brownian meander.

AB - This paper is concerned with the integration by parts formulae for the pinned or the standard Wiener measures restricted on a space of paths staying between two curves. The boundary measures, concentrated on the set of paths touching one of the curves once, are specified. Our approach is based on the polygonal approximations. In particular, to establish the convergence of boundary terms, a uniform estimate is derived by means of comparison argument for a sequence of random walks conditioned to stay between two polygons. Applying the Brascamp-Lieb inequality, the stochastic integrals of Wiener type are constructed relative to the three-dimensional Bessel bridge or the Brownian meander.

KW - 3D Bessel bridge

KW - Brascamp-Lieb inequality

KW - Brownian meander

KW - Integration by parts and Wiener measure

KW - SPDE with reflection

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U2 - 10.1007/s00440-006-0010-9

DO - 10.1007/s00440-006-0010-9

M3 - Article

AN - SCOPUS:33845900932

VL - 137

SP - 289

EP - 321

JO - Probability Theory and Related Fields

JF - Probability Theory and Related Fields

SN - 0178-8051

IS - 3-4

ER -