## Journal of Mathematics of Kyoto University

### Brownian motion conditioned to stay in a cone

Rodolphe Garbit

#### Abstract

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.

#### Article information

Source
J. Math. Kyoto Univ., Volume 49, Number 3 (2009), 573-592.

Dates
First available in Project Euclid: 16 December 2009

https://projecteuclid.org/euclid.kjm/1260975039

Digital Object Identifier
doi:10.1215/kjm/1260975039

Mathematical Reviews number (MathSciNet)
MR2583602

Zentralblatt MATH identifier
1192.60091

Subjects