On the local times of noise reinforced Bessel processes
Annales Henri Lebesgue, Volume 5 (2022), pp. 1277-1294.

KeywordsScaling limits, Bessel process, stochastic reinforcement, self-similar Markov process

### Abstract

We investigate the effects of noise reinforcement on a Bessel process of dimension $d\in \left(0,2\right)$, 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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