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

Tadahisa Funaki, Kensuke Ishitani

Research output: Contribution to journalArticle

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 languageEnglish
Pages (from-to)289-321
Number of pages33
JournalProbability Theory and Related Fields
Volume137
Issue number3-4
DOIs
Publication statusPublished - 2007 Mar
Externally publishedYes

Fingerprint

Integration by Parts Formula
Wiener Measure
Path Space
Polygonal Approximation
Path
Curve
Uniform Estimates
Stochastic Integral
Friedrich Wilhelm Bessel
Polygon
Random walk
Three-dimensional
Term
Standards
Integral
Approximation

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

Cite this

Integration by parts formulae for Wiener measures on a path space between two curves. / Funaki, Tadahisa; Ishitani, Kensuke.

In: Probability Theory and Related Fields, Vol. 137, No. 3-4, 03.2007, p. 289-321.

Research output: Contribution to journalArticle

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