使用算子缩放的建模和仿真
Modeling and simulation with operator scaling
摘要：
自相似过程在模拟具有标度特性的各种现象时非常有用。运算符缩放允许在每个坐标中使用不同的缩放因子。本文发展了实用的方法建模和模拟随机过程的算子标度。基于级数表示和小跳跃的高斯近似，提出了算子稳定Levy过程的一种模拟方法。给出了几个例子来说明实际应用。根据二维算子稳定Levy过程的指数和对称群，给出了二维算子稳定Levy过程的一种分类。最后，我们的一些意见和一般运营商的自相似过程的扩展。
英文摘要：
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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