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Elsevier, Stochastic Processes and their Applications, 12(120), p. 2390-2411, 2010

DOI: 10.1016/j.spa.2010.08.002

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Modeling and simulation with operator scaling

Journal article published in 2010 by Serge Cohen, Mark M. Meerschaert, Jan Rosinski
This paper is made freely available by the publisher.
This paper is made freely available by the publisher.

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Abstract

Self-similar processes are useful in modeling diverse phenomena that exhibit scaling properties. Operator scaling allows a different scale factor in each coordinate. This paper develops practical methods for modeling and simulating stochastic processes with operator scaling. A simulation method for operator stable Levy processes is developed, based on a series representation, along with a Gaussian approximation of the small jumps. Several examples are given to illustrate practical applications. A classification of operator stable Levy processes in two dimensions is provided according to their exponents and symmetry groups. We conclude with some remarks and extensions to general operator self-similar processes. ; Comment: 29 pages, 13 figures