Abstract
We introduce a new diffusion process which arises as the limit of a Bessel process of dimension conditioned upon remaining bounded below one until time n. In addition to being interesting in its own right, we argue that the resulting diffusion process is a natural hard edge counterpart to the Ferrari-Spohn diffusion of [9]. In particular, we show that the generator of our new diffusion has the same relation to the Sturm-Liouville problem for the Bessel operator that the Ferrari-Spohn diffusion does to the corresponding problem for the Airy operator.
Funding Statement
The author was supported by the NSF Graduate Research fellowship under grant #1745302.
Acknowledgments
The author would like to thank Alexei Borodin for helpful feedback and bringing the similarity between Ferrari-Spohn diffusions and [11] to his attention. The author would also like to thank the anonymous referee for their careful reading of this article.
Citation
Matthew Lerner-Brecher. "Bounded Bessel processes and Ferrari-Spohn diffusions." Electron. Commun. Probab. 28 1 - 9, 2023. https://doi.org/10.1214/23-ECP568
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