Modeling and simulation with operator scaling
AbstractSelf-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 Lévy 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.
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Bibliographic InfoArticle provided by Elsevier in its journal Stochastic Processes and their Applications.
Volume (Year): 120 (2010)
Issue (Month): 12 (December)
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Web page: http://www.elsevier.com/wps/find/journaldescription.cws_home/505572/description#description
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- Meerschaert, Mark M. & Xiao, Yimin, 2005. "Dimension results for sample paths of operator stable Lévy processes," Stochastic Processes and their Applications, Elsevier, vol. 115(1), pages 55-75, January.
- Meerschaert, Mark M. & Scheffler, Hans-Peter, 2008. "Triangular array limits for continuous time random walks," Stochastic Processes and their Applications, Elsevier, vol. 118(9), pages 1606-1633, September.
- Meerschaert, Mark M. & Alan Veeh, Jeery, 1995. "Symmetry groups in d-space," Statistics & Probability Letters, Elsevier, vol. 22(1), pages 1-6, January.
- Meerschaert, Mark M. & Scalas, Enrico, 2006.
"Coupled continuous time random walks in finance,"
Physica A: Statistical Mechanics and its Applications,
Elsevier, vol. 370(1), pages 114-118.
- Sato, Ken-iti, 1987. "Strictly operator-stable distributions," Journal of Multivariate Analysis, Elsevier, vol. 22(2), pages 278-295, August.
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