Modeling and simulation with operator scaling

Details Modeling and simulation with operator scaling Modeling and simulation with operator scaling

2009-12-24

arxiv.org/abs/0912.4784v1

Mathematics

Probability

29 pages, 13 figures

Scientific paper

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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