Summary
We study some features concerning the occupation timeA t of a d-dimensional coneC by Brownian motion. In particular, in the case whereC is convex, we investigate the asymptotic behaviour ofP(A1<u) asu→0, when the Brownian motion starts at the vertex ofC. We also give the precise integral test, which decides whether a.s., lim inf t→∞ A t/(tf(t))=0 or ∞ for a decreasing functionf.
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Meyre, T., Werner, W. On the occupation times of cones by Brownian motion. Probab. Th. Rel. Fields 101, 409–419 (1995). https://doi.org/10.1007/BF01200504
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DOI: https://doi.org/10.1007/BF01200504
Mathematics Subject Classification (1991)
- 60J65
- 60G17