Modeling and simulation with operator scaling

被引：8

作者：

Cohen, Serge ^{[2
]}

Meerschaert, Mark M. ^{[1
]}

Rosinski, Jan ^{[3
]}

机构：

[1] Michigan State Univ, Dept Stat & Probabil, E Lansing, MI 48824 USA

[2] Univ Toulouse 3, Inst Math Toulouse, Univ Toulouse, F-31062 Toulouse, France

[3] Univ Tennessee, Dept Math, Knoxville, TN 37996 USA

来源：

STOCHASTIC PROCESSES AND THEIR APPLICATIONS | 2010年 / 120卷 / 12期

关键词：

Levy processes; Gaussian approximation; Shot noise series expansions; Simulation; Tempered stable processes; Operator stable processes; APPROXIMATION;

D O I：

10.1016/j.spa.2010.08.002

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

Self-similar processes are useful models for natural systems that exhibit scaling. Operator scaling allows a different scale factor in each coordinate. This paper develops practical methods for modeling and simulation. A simulation method is developed for operator scaling Levy processes, based on a series representation, along with a Gaussian approximation of the small jumps. Several examples are given to illustrate the range of practical applications. A complete characterization of symmetries in two dimensions is given, for any exponent and spectral measure, to inform the choice of these model parameters. The paper concludes with some extensions to general operator self-similar processes. (C) 2010 Elsevier B.V. All rights reserved.

引用

页码：2390 / 2411

页数：22

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