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arXiv · 0912.4784

Modeling and simulation with operator scaling

Serge Cohen·Mark M. Meerschaert·Jan Rosinski
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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.

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Serge Cohen, Mark M. Meerschaert, Jan Rosinski. 2009-12-24. Modeling and simulation with operator scaling. https://arxiv.org/abs/0912.4784

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