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

We investigate the effects of noise reinforcement on a Bessel process of dimension d(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.

On étudie les effects du renforcement du bruit sur un processus de Bessel de dimension d(0,2), et plus précisément sur le comportement asymptotique de ses fonctionnelles additives. Cela nous conduit à introduire le processus du temps local et son inverse. Nous identifions ce dernier comme un processus de Markov (homogène en temps) auto-similaire, ce qui conduit à plusieurs résultats explicites.

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Accepted:
Published online:
DOI: 10.5802/ahl.151
Classification: 60J55, 60J60
Keywords: Scaling limits, Bessel process, stochastic reinforcement, self-similar Markov process
Bertoin, Jean 1

1 Institute of Mathematics, University of Zurich, (Switzerland)
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Bertoin, Jean. On the local times of noise reinforced Bessel processes. Annales Henri Lebesgue, Volume 5 (2022), pp. 1277-1294. doi : 10.5802/ahl.151. http://www.numdam.org/articles/10.5802/ahl.151/

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