On Brownian flights

Athanasios Batakis (1) , Pierre Levitz (2) , Michel Zinsmeister (1, 2)

1 MAPMO - Mathématiques - Analyse, Probabilités, Modélisation - Orléans
2 LPMC - Laboratoire de physique de la matière condensée

Let K be a compact subset of ${\mathbb R}^n$. We choose at random with uniform law a point at distance $\varepsilon$ of K and start a Brownian motion (BM) from this point. We study the probability that this BM hits K for the first time at a distance $\geq r$ from the starting point.

Mots clés: Brownian motion; Brownian flights; diffusion of fractals

Domaines: Analyse classique [math.CA]

Athanasios Batakis, Pierre Levitz, Michel Zinsmeister. On Brownian flights. Pure and Applied Mathematics Quarterly, 2011, Vol. 7, 1, pg 85-105. ⟨hal-00142289⟩