Modeling and simulation with operator scaling

TL;DR

This paper develops methods for modeling and simulating operator scaled self-similar stochastic processes, including stable Levy processes, with practical examples and classifications.

Contribution

It introduces a simulation approach for operator stable Levy processes using series representation and Gaussian approximation, advancing modeling capabilities.

Findings

A series-based simulation method for operator stable Levy processes.

Classification of 2D operator stable Levy processes by exponents and symmetry.

Practical applications demonstrated through examples.

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.