Brownian motion conditioned to stay in a cone

Rodolphe Garbit (1)

1 LMJL - Laboratoire de Mathématiques Jean Leray

A result of R. Durrett, D. Iglehart and D. Miller states that Brownian meander is Brownian motion conditioned to stay positive for a unit of time, in the sense that it is the weak limit, as $x$ goes to $0$, of Brownian motion started at $x>0$ and conditioned to stay positive for a unit of time. We extend this limit theorem to the case of multidimensional Brownian motion conditioned to stay in a smooth convex cone. Properties of the limit process are obtained and applications to random walks are given.

Mots clés: conditioned Brownian motion; limit theorems

Domaines: Probabilités [math.PR]

Rodolphe Garbit. Brownian motion conditioned to stay in a cone. 2008. ⟨hal-00341032v1⟩