### 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 |
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Pages (from-to) | 289-321 |

Number of pages | 33 |

Journal | Probability Theory and Related Fields |

Volume | 137 |

Issue number | 3-4 |

DOIs | |

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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## Cite this

*Probability Theory and Related Fields*,

*137*(3-4), 289-321. https://doi.org/10.1007/s00440-006-0010-9