The area of spheres in the Brownian plane
Probability
2025-07-09 v2
Abstract
We consider the area of spheres centered at the distinguished point in the Brownian plane. As a function of the radius, the resulting process has continuously differentiable sample paths. Furthermore, the pair consisting of the process and its derivative is time-homogeneous Markov and satisfies an explicit stochastic differential equation.
Keywords
Cite
@article{arxiv.2504.15860,
title = {The area of spheres in the Brownian plane},
author = {Jean-François Le Gall},
journal= {arXiv preprint arXiv:2504.15860},
year = {2025}
}
Comments
Revised version, incorporating suggestions of the referee, 20 pages