×

zbMATH — the first resource for mathematics

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
PDF BibTeX XML Cite
Full Text: DOI Euclid