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arXiv · 2109.12521

On the local times of noise reinforced Bessel processes

Jean Bertoin
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Abstract

We investigate the effects of noise reinforcement on a Bessel process of dimension $d\in(0,2)$, and more specifically on the asymptotic behavior of its additive functionals. This leads us to introduce a local time process and its inverse. We identify the latter as an increasing self-similar (time-homogeneous) Markov process, and from this, several explicit results can be deduced.

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Jean Bertoin. 2021-09-26. On the local times of noise reinforced Bessel processes. https://arxiv.org/abs/2109.12521

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