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arXiv · 1609.02438

Integration by parts on the law of the modulus of the Brownian bridge

Martin Grothaus·Robert Voßhall
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Abstract

We prove an infinite dimensional integration by parts formula on the law of the modulus of the Brownian bridge $BB=(BB_t)_{0 \leq t \leq 1}$ from $0$ to $0$ in use of methods from white noise analysis and Dirichlet form theory. Additionally to the usual drift term, this formula contains a distribution which is constructed in the space of Hida distributions by means of a Wick product with Donsker's delta (which correlates with the local time of $|BB|$ at zero). This additional distribution corresponds to the reflection at zero caused by the modulus.

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Martin Grothaus, Robert Voßhall. 2016-09-08. Integration by parts on the law of the modulus of the Brownian bridge. https://arxiv.org/abs/1609.02438

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