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

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Abstract

We prove an infinite dimensional integration by parts formula on the law of the modulus of the Brownian bridge \(BB=(BB_t)_{0 \le t \le 1}\) 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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Acknowledgements

Financial support by the DFG through the project GR 1809/14-1 is gratefully acknowledged.

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  1. University of Kaiserslautern, P.O. Box 3049, 67653, Kaiserslautern, Germany

    Martin Grothaus & Robert Vosshall

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  1. Martin Grothaus
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  2. Robert Vosshall
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Correspondence to Robert Vosshall.

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Grothaus, M., Vosshall, R. Integration by parts on the law of the modulus of the Brownian bridge. Stoch PDE: Anal Comp 6, 335–363 (2018). https://doi.org/10.1007/s40072-018-0110-4

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