On the occupation times of cones by Brownian motion |
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| Authors: | Thierry Meyre Wendelin Werner |
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| Affiliation: | (1) U.F.R. de Mathématiques, Université Paris VII, 2 place Jussieu, F-75251 Paris Cedex 05, France;(2) Statistical Laboratory, D.P.M.M.S., C.N.R.S. and University of Cambridge, 16 Mill Lane, CB2 1SB Cambridge, England |
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| Abstract: | Summary We study some features concerning the occupation timeAt of a d-dimensional coneC by Brownian motion. In particular, in the case whereC is convex, we investigate the asymptotic behaviour ofP(A1u 0, when the Brownian motion starts at the vertex ofC. We also give the precise integral test, which decides whether a.s., lim inft At/(tf(t))=0 or for a decreasing functionf. |
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| Keywords: | 60J65 60G17 |
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