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

Tadahisa Funaki; Kensuke Ishitani

doi:10.1007/s00440-006-0010-9

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

Tadahisa Funaki, Kensuke Ishitani

Research output: Contribution to journal › Article › peer-review

10 Citations (Scopus)

Abstract

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.

Original language	English
Pages (from-to)	289-321
Number of pages	33
Journal	Probability Theory and Related Fields
Volume	137
Issue number	3-4
DOIs	https://doi.org/10.1007/s00440-006-0010-9
Publication status	Published - 2007 Mar 1
Externally published	Yes

Keywords

3D Bessel bridge
Brascamp-Lieb inequality
Brownian meander
Integration by parts and Wiener measure
SPDE with reflection

ASJC Scopus subject areas

Analysis
Statistics and Probability
Statistics, Probability and Uncertainty

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