### 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 | |

Publication status | Published - 2007 Mar |

Externally published | Yes |

### Fingerprint

### 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

*Probability Theory and Related Fields*,

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

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

Research output: Contribution to journal › Article

*Probability Theory and Related Fields*, vol. 137, no. 3-4, pp. 289-321. https://doi.org/10.1007/s00440-006-0010-9

}

TY - JOUR

T1 - Integration by parts formulae for Wiener measures on a path space between two curves

AU - Funaki, Tadahisa

AU - Ishitani, Kensuke

PY - 2007/3

Y1 - 2007/3

N2 - 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.

AB - 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.

KW - 3D Bessel bridge

KW - Brascamp-Lieb inequality

KW - Brownian meander

KW - Integration by parts and Wiener measure

KW - SPDE with reflection

UR - http://www.scopus.com/inward/record.url?scp=33845900932&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=33845900932&partnerID=8YFLogxK

U2 - 10.1007/s00440-006-0010-9

DO - 10.1007/s00440-006-0010-9

M3 - Article

AN - SCOPUS:33845900932

VL - 137

SP - 289

EP - 321

JO - Probability Theory and Related Fields

JF - Probability Theory and Related Fields

SN - 0178-8051

IS - 3-4

ER -