Abstract
We generalise the integration by parts formulae obtained in a recent work with Zambotti to Bessel bridges on 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.
Acknowledgments
I am especially indebted to Lorenzo Zambotti for introducing me to this research topic as well as countless precious discussions. The arguments used in Prop 4.1 below to show quasi-regularity of the forms associated with the law of a Bessel bridge of dimension 2 were communicated to me by Rongchan Zhu and Xiangchan Zhu, whom I warmly thank. Work on this article started as I was completing my PhD at the Laboratoire de Probabilités, Statistique et Modélisation (UMR 8001) at Sorbonne Université, Paris.
Citation
Henri Elad Altman. "Bessel SPDEs with general Dirichlet boundary conditions." Electron. J. Probab. 26 1 - 36, 2021. https://doi.org/10.1214/21-EJP632
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