NDLI: Dynamics of Mandelbrot cascades

Content Provider	Springer Nature Link
Author	Barral, Julien Peyrière, Jacques Wen, Zhi Ying
Copyright Year	2008
Abstract	Mandelbrot multiplicative cascades provide a construction of a dynamical system on a set of probability measures defined by inequalities on moments. To be more specific, beyond the first iteration, the trajectories take values in the set of fixed points of smoothing transformations (i.e., some generalized stable laws). Studying this system leads to a central limit theorem and to its functional version. The limit Gaussian process can also be obtained as limit of an “additive cascade” of independent normal variables.
Ending Page	631
Page Count	17
Starting Page	615
File Format	PDF
ISSN	01788051
e-ISSN	14322064
Journal	Probability Theory and Related Fields
Issue Number	3
Volume Number	144
Language	English
Publisher	Springer-Verlag
Publisher Date	2008-05-14
Publisher Place	Berlin/Heidelberg
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Mathematical and Computational Physics Functional limit theorems; invariance principles Probability Theory and Stochastic Processes Martingales with discrete parameter Dynamical systems Quantitative Finance Multiplicative cascades Mandelbrot martingales Random fractals Statistics for Business/Economics/Mathematical Finance/Insurance Additive cascades Operations Research/Decision Theory Functional central limit theorem Gaussian processes Mathematical Biology in General Central limit and other weak theorems Sample path properties
Content Type	Text
Resource Type	Article
Subject	Statistics and Probability Analysis Statistics, Probability and Uncertainty

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