Abstract
We generalise the integration by parts formulae obtained in a recent work with Zambotti to Bessel bridges on [0,1] with arbitrary boundary values, as well as Bessel processes with arbitrary initial conditions. This allows us to write, formally, the corresponding dynamics using renormalised local times, thus extending the Bessel SPDEs of [7] to general Dirichlet boundary conditions. We also prove a dynamical result for the case of dimension 2, by providing a construction of the stationary dynamics corresponding to the law of a 2-dimensional Bessel bridge.
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