Brownian motion conditioned to stay in a cone

Details Brownian motion conditioned to stay in a cone Brownian motion conditioned to stay in a cone

2008-11-25

arxiv.org/abs/0811.4079v3

Mathematics

Probability

Scientific paper

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.

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