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

Tadahisa Funaki*, Kensuke Ishitani

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

10 Citations (Scopus)


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
Issue number3-4
Publication statusPublished - 2007 Mar
Externally publishedYes


  • 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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