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Integration by Parts Formulae for Wiener Measures on a Path Space between two Curves
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  • Published: 17 June 2006

Integration by Parts Formulae for Wiener Measures on a Path Space between two Curves

  • Tadahisa Funaki1 &
  • Kensuke Ishitani1 

Probability Theory and Related Fields volume 137, pages 289–321 (2007)Cite this article

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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.

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Author information

Authors and Affiliations

  1. Graduate School of Mathematical Sciences, The University of Tokyo, Komaba, Tokyo, 153-8914, Japan

    Tadahisa Funaki & Kensuke Ishitani

Authors
  1. Tadahisa Funaki
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  2. Kensuke Ishitani
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Corresponding author

Correspondence to Tadahisa Funaki.

Additional information

Supported in part by the JSPS Grant (B)(1)14340029

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Cite this article

Funaki, T., Ishitani, K. Integration by Parts Formulae for Wiener Measures on a Path Space between two Curves. Probab. Theory Relat. Fields 137, 289–321 (2007). https://doi.org/10.1007/s00440-006-0010-9

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  • Received: 23 February 2005

  • Revised: 20 December 2005

  • Published: 17 June 2006

  • Issue Date: March 2007

  • DOI: https://doi.org/10.1007/s00440-006-0010-9

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Keywords

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

Mathematics Subject Classification (2000)

  • Primary 60H07
  • Secondary 60H15
  • 31C25
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