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

2016/09/08 by Grothaus, Martin, Voßhall, Robert
#31C25 #46F25 #60H07 #60H40 #FOS: Mathematics #Functional Analysis (math.FA) #Probability (math.PR)

paper · doi:10.48550/arxiv.1609.02438

Abstract

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