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DISTRIBUTION OF BROWNIAN LOCAL TIME ON CURVES

Published online by Cambridge University Press:  01 March 1998

BURGESS DAVIS
BURGESS DAVIS
Affiliation:
Department of Statistics, Purdue University, West Lafayette, IN 47907-1399, USA
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Abstract

For all smooth nondecreasing functions f on [0, 1], the local time Lf spent by standard Brownian motion on the graph of f satisfies P(Lf<x) [ges ]P(2L0<x), for x>0. The constant 2 in this inequality may not be replaced with a smaller one.

Type
Research Article
Information
Bulletin of the London Mathematical Society , Volume 30 , Issue 2 , March 1998 , pp. 182 - 184
Copyright
© The London Mathematical Society 1998

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