Linear fractional stable sheets: Wavelet expansion and sample path properties

Antoine Ayache, François Roueff and Yimin Xiao

Stochastic Processes and their Applications, 2009, vol. 119, issue 4, 1168-1197

Abstract: In this paper we give a detailed description of the random wavelet series representation of real-valued linear fractional stable sheet introduced in [A. Ayache, F. Roueff, Y. Xiao, Local and asymptotic properties of linear fractional stable sheets, C.R. Acad. Sci. Paris Ser. I. 344 (6) (2007) 389-394]. By using this representation, in the case where the sample paths are continuous, an anisotropic uniform and quasi-optimal modulus of continuity of these paths is obtained as well as an upper bound for their behavior at infinity and around the coordinate axes. The Hausdorff dimensions of the range and graph of these stable random fields are then derived.

Keywords: Wavelet; analysis; Stable; processes; Linear; fractional; stable; sheet; Modulus; of; continuity; Hausdorff; dimension (search for similar items in EconPapers)
Date: 2009
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Citations: View citations in EconPapers (10)

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