Bounded Bessel Processes and Ferrari-Spohn Diffusions

2023/07/12 by Matthew Lerner-Brecher, Lerner-Brecher, Matthew
Economics, Econometrics and Finance · Mathematics · #34B24 #60J60 #FOS: Mathematics #Probability (math.PR) #Spectral Theory in Mathematical Physics #Stochastic processes and financial applications #Stochastic processes and statistical mechanics

paper · pdf · doi:10.48550/arxiv.2307.06493

openalex publication_date 2023/07/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We introduce a new diffusion process which arises as the n→∞ limit of a Bessel process of dimension d ≥ 2 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 arXiv:math/0308242. 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.

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