The average density of the path of planar Brownian motion

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.

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Year of publication:	1998
Authors:	Mörters, Peter
Published in:	Stochastic Processes and their Applications. - Elsevier, ISSN 0304-4149. - Vol. 74.1998, 1, p. 133-149
Publisher:	Elsevier
Keywords:	Brownian motion Occupation measure Average density Logarithmic averages Density distribution Pathwise Kallianpur-Robbins law

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Type of publication:	Article
Source:	RePEc - Research Papers in Economics

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