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Brownian motion conditioned to stay in a cone. (English) Zbl 1192.60091
Summary: A result of R. T. Durrett, D. L. Iglehart and D. R. Miller [Ann. Probab. 5, 117–129 (1977; Zbl 0356.60034)] 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.

##### MSC:
 60J65 Brownian motion 60B10 Convergence of probability measures
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