Random fields of variable order on multifractal domains

Ruiz-Medina, Maria D., Anh, Vo V., & Angulo, Jose M. (2004) Random fields of variable order on multifractal domains. [Working Paper] (Unpublished)

Abstract

We introduce a class of random …eld models with variable regularity/singularity order on multifractal domains. The derivation of results on atomic decomposition of functions in fractional Sobolev spaces of variable order, and traces of these spaces on multifractal domains plays a key role. The non-triviality of the multifractal spectrum of the measure de…ning the multifractal domain ensures the non-triviality of the multifractal spectrum of the functions in the trace Sobolev spaces of variable order de…ned. The generalized reproducing kernel Hilbert space theory is considered to introduce a class of random …elds with non-trivial mean-square multifractal spectrum. In the Gaussian case, the random …eld models studied have multifractal sample paths.

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ID Code: 493
Item Type: Working Paper
Refereed: No
Keywords: Random fields, variable order, multifractal domains
Subjects: Australian and New Zealand Standard Research Classification > MATHEMATICAL SCIENCES (010000) > STATISTICS (010400) > Statistical Theory (010405)
Australian and New Zealand Standard Research Classification > MATHEMATICAL SCIENCES (010000) > STATISTICS (010400)
Divisions: Past > QUT Faculties & Divisions > Faculty of Science and Technology
Past > Schools > Mathematical Sciences
Copyright Owner: Copyright 2004 The Authors
Deposited On: 09 Dec 2005
Last Modified: 15 Feb 2015 23:57

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