English

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