The average density of the path of planar Brownian motion

Peter Mörters

Stochastic Processes and their Applications, 1998, vol. 74, issue 1, 133-149

Abstract: We show that the occupation measure on the path of a planar Brownian motion run for an arbitrary finite time interval has an average density of order three with respect to the gauge function . In other words, almost surely,We also prove a refinement of this statement: Almost surely, at -almost every ,in other words, the distribution of the -density function under the averaging measures of order three converges to a gamma distribution with parameter two.

Keywords: Brownian; motion; Occupation; measure; Average; density; Logarithmic; averages; Density; distribution; Pathwise; Kallianpur-Robbins; law (search for similar items in EconPapers)
Date: 1998
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