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.
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 $BB=(BB_t)_{0 \leq t \leq 1}$ 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
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.