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

Martin Grothaus; Robert Vo{\ss}hall

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

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arxiv 1609.02438 v2 pith:HNWP5G5Z submitted 2016-09-08 math.PR math.FA

Martin Grothaus , Robert Vo{ss}hall This is my paper · ORCID

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keywords modulusbridgebrowniandistributionformulaintegrationpartszero

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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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Bessel SPDEs with general Dirichlet boundary conditions
math.PR 2019-08 conditional novelty 6.0 of 10

The paper proves generalized integration by parts formulas for Bessel bridges with arbitrary boundary values and constructs a weak gradient dynamics for the two-dimensional Bessel bridge.

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