Hostname: page-component-848d4c4894-5nwft Total loading time: 0 Render date: 2024-05-07T09:11:49.067Z Has data issue: false hasContentIssue false

On the Hausdorff dimension of Brownian cone points

Published online by Cambridge University Press:  24 October 2008

Steven N. Evans
Affiliation:
Statistical Laboratory, University of Cambridge

Extract

Let B(t) be a two-dimensional Brownian motion. For 0 < α < 2π, set

and, for 0 ≥ β< 2π, let F(α,β) be F(α) rotated through an angle β about the origin.

Type
Research Article
Copyright
Copyright © Cambridge Philosophical Society 1985

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

[1]Blumenthal, R. M. and Getoor, R. K.. Markov Processes and Potential Theory (Academic Press, 1968).Google Scholar
[2]Debreu, G.. Integration of correspondences. Proc. Fifth Berkeley Symp. Math. Statist, and Probability 2 (1966), 351372.Google Scholar
[3]Kaufman, R.. Une propriété métrique du mouvement brownien. C.R. Acad. Sci. Paris 268 (A) (1969), 727728.Google Scholar
[4]Perkins, E.. On the Hausdorff dimension of Brownian slow points. Z. wahrsch. Verw. Gebiete 64 (1983), 369399.CrossRefGoogle Scholar
[5]Rockafeller, R. T.. Convex Analysis, Princeton Mathematical Series, 28 (Princeton University Press, 1970).CrossRefGoogle Scholar
[6]Shimura, M.. Exursions in a cone for two-dimensional Brownian motion (preprint).Google Scholar
[7]Taylor, S. J.. Multiple points for the sample paths of the symmetric stable process. Z. Wahrsch. Verw. Gebiete 5 (1966), 247264.CrossRefGoogle Scholar
[8]Uchiyama, K.. Brownian first exit from, and sojourn over, one sided moving boundary and application. Z. Wahrsch. Verw. Gebiete 54 (1980), 75116.CrossRefGoogle Scholar