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

N. Patzschke and M. Zähle

Stochastic Processes and their Applications, 1993, vol. 45, issue 1, 61-72

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.

Date: 1993
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