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

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.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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