Meeting of squared Bessel flow lines and application to the skew Brownian motion

2024/11/07 by Aïdékon, Elie, Wang, Chengshi, Yu, Yaolin
#FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.2411.04773

Abstract

We study the meeting level between squared Bessel (BESQ) flow lines of different dimensions, and show that it gives rise to a jump Markov process. We apply these results to the skew Brownian flow introduced by Burdzy and Chen \citeburdzy2001local and Burdzy and Kaspi \citeburdzy2004lenses. It allows us to extend the results of \citeburdzy2001local and of Gloter and Martinez \citegloter2013distance describing the local time flow of skew Brownian motions. Finally, we compute the Hausdorff dimension of exceptional times revealed by Burdzy and Kaspi \citeburdzy2004lenses when skew Brownian flow lines bifurcate.

Related

• Squared Bessel processes of positive and negative dimension embedded in\n Brownian local times
• A stochastic flow arising in the study of local times
• Inside the nature of squared Bessel process
• Lenses in Skew Brownian Flow
• Bessel process, Schramm-Loewner evolution, and Dyson model