Hausdorff-type measures of the sample paths of fractional Brownian motion

Yimin Xiao

Stochastic Processes and their Applications, 1998, vol. 74, issue 2, 251-272

Abstract: Let [phi] be a Hausdorff measure function and let [Lambda] be an infinite increasing sequence of positive integers. The Hausdorff-type measure [phi]-m[Lambda] associated to [phi] and [Lambda] is studied. Let be fractional Brownian motion of index [alpha] in We evaluate the exact [phi]-m[Lambda] measure of the image and graph set of X(t). A necessary and sufficient condition on the sequence [Lambda] is given so that the usual Hausdorff measure functions for X([0,1]N) and Gr X([0,1]N) are still the correct measure functions. If the sequence [Lambda] increases faster, then some smaller measure functions will give positive and finite ([phi],[Lambda])-Hausdorff measure for X([0,1]N) and Gr X([0,1]N)

Keywords: Fractional; Brownian; motion; Image; Graph; set; Hausdorff-type; measures; Packing; measure (search for similar items in EconPapers)
Date: 1998
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