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The average density of the path of planar Brownian motion

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  • Mörters, Peter

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.

Suggested Citation

  • Mörters, Peter, 1998. "The average density of the path of planar Brownian motion," Stochastic Processes and their Applications, Elsevier, vol. 74(1), pages 133-149, May.
    • Handle: RePEc:eee:spapps:v:74:y:1998:i:1:p:133-149
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    References listed on IDEAS

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    1. Falconer, K. J. & Xiao, Y. M., 1995. "Average densities of the image and zero set of stable processes," Stochastic Processes and their Applications, Elsevier, vol. 55(2), pages 271-283, February.
    2. Patzschke, N. & Zähle, M., 1993. "Fractional differentiation in the self-affine case II - Extremal processes," Stochastic Processes and their Applications, Elsevier, vol. 45(1), pages 61-72, March.
    3. Patzschke, N. & Zähle, M., 1992. "Fractional differentiation in the self-affine case I - Random functions," Stochastic Processes and their Applications, Elsevier, vol. 43(1), pages 165-175, November.
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    1. Falconer, K. J. & Xiao, Y. M., 1995. "Average densities of the image and zero set of stable processes," Stochastic Processes and their Applications, Elsevier, vol. 55(2), pages 271-283, February.

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