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Large increments of Brownian motion

Published online by Cambridge University Press:  22 January 2016

R. Kaufman
R. Kaufman*
Affiliation:
University of Illinois
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Let X(t) denote Brownian motion on the line 0 ≤ t < ∞, let and let 0 < α < 1. Orey and Taylor [5] have investigated the random set defined by the inequalities

and proved that P{dim Eα = 1 – α2} = 1. Here we prove two theorems on Eα that reflect more subtle properties of Eα than its Hausdorff dimension alone.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 56 , January 1975 , pp. 139 - 145
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1975

References

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