Journal of Mathematics of Kyoto University

Brownian motion conditioned to stay in a cone

Rodolphe Garbit

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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

Permanent link to this document
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
Primary: 60J65: Brownian motion [See also 58J65]
Secondary: 60B10: Convergence of probability measures

Citation

Garbit, Rodolphe. Brownian motion conditioned to stay in a cone. J. Math. Kyoto Univ. 49 (2009), no. 3, 573--592. doi:10.1215/kjm/1260975039. https://projecteuclid.org/euclid.kjm/1260975039


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