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Fractional differentiation in the self-affine case II - Extremal processes

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  • Patzschke, N.
  • Zähle, M.

Abstract

In Part I we introduced the concept of fractional Cesàro derivatives of random processes. We proved that they exist for self-affine functions at Lebesgue-a.a. points. In the present part we consider together with the random process a random measure and give conditions which ensure that the fractional Cesàro derivative exists at almost all points w.r.t. this random measure. Our conditions are satisfied by the measure associated with the maximal process of a self-affine process, so we deduce that the Cesàro derivative exists at almost all points of increase.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:spapps:v:45:y:1993:i:1:p:61-72
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    Cited by:

    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. 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.

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