Average densities of the image and zero set of stable processes

K. J. Falconer and Y. M. Xiao

Stochastic Processes and their Applications, 1995, vol. 55, issue 2, 271-283

Abstract: The 'order-two' or 'average' density of a measure [mu] at a point x is defined as limT --> x(1/T)[integral operator]T0[mu](B(x, e-s))e[alpha]sds for appropriate [alpha]. We show that, with probability one, the order-two density of the natural measure [mu] on the image set or zero set of a wide class of stable processes exists and takes the same value almost everywhere in the support of [mu]. We calculate this value in certain cases.

Keywords: 28A75; 58F11; 60G17; 60J30; Stable; processes; Image; Zero; set; Order-two; density; Hausdorff; measure (search for similar items in EconPapers)
Date: 1995
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Citations: View citations in EconPapers (1)

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