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

Martin Grothaus, Robert Voßhall

Published 2016-09-08Version 1

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 in use 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.