A multifractal system is a generalization of a fractal system in which a single exponent (the fractal dimension) is not enough to describe its dynamics;...

application of statistical methods to economic data), the Markov-switching multifractal (MSM) is a model of asset returns developed by Laurent E. Calvet and...

the Koch snowflake. Qualitative self-similarity: as in a time series Multifractal scaling: characterized by more than one fractal dimension or scaling...

studies of participation numbers obtained by exact diagonalization, multifractal properties, level statistics and many others. Especially fruitful is...

\alpha (q)} . DFA is the special case where q = 2 {\displaystyle q=2} . Multifractal systems scale as a function F q ( n ) ∝ n α ( q ) {\displaystyle F_{q}(n)\propto...

dynamics he is known for having introduced, together with Uriel Frisch, multifractal models to describe the phenomenon of intermittency in turbulent flows...

Missouri Morehouse School of Medicine, Atlanta, Georgia Markov switching multifractal, a model of asset returns Method of simulated moments, in econometrics...

1 {\displaystyle H_{q}=1} for q ≥ α {\displaystyle q\geq \alpha } . Multifractal detrended fluctuation analysis is one method to estimate H ( q ) {\displaystyle...

Calvet, L. E. (1997). A multifractal model of asset returns. 3.2 The Binomial Measure is the Simplest Example of a Multifractal Except the trivial case...

{\displaystyle D={\frac {d\ \log(L(k))}{d\ \log(k)}}} Lyapunov dimension Multifractal dimensions: a special case of Rényi dimensions where scaling behaviour...

expansions and recessions). A more recent example is the Markov switching multifractal model of Laurent E. Calvet and Adlai J. Fisher, which builds upon the...

2307/2159830. JSTOR 2159830. Falconer, Kenneth J. (2004-01-01). "One-sided multifractal analysis and points of non-differentiability of devil's staircases"....

model Stochastic volatility jump SABR volatility model Markov switching multifractal The Greeks Finite difference methods for option pricing Vanna–Volga pricing...

universe itself, is a fractal across a wide range of scales (see also: multifractal system). More generally, it relates to the usage or appearance of fractals...

1086/497125. S2CID 14905675. Mureika, J. R. & Dyer, C. C. (2004). "Review: Multifractal Analysis of Packed Swiss Cheese Cosmologies". General Relativity and...

S2CID 14240006. Meakin, Paul (1987). "Diffusion-limited aggregation on multifractal lattices: A model for fluid-fluid displacement in porous media". Physical...

In mathematics, a multiplicative cascade is a fractal/multifractal distribution of points produced via an iterative and multiplicative random process....

the purely empirical ETAS linear model. The basic assumption of this "Multifractal stress activated" model is that, at any place and time, the local failure...

that produces the Sierpiński triangle. Ornstein and others describe a multifractal system, where instead of working in a fixed base, one works in a variable...

Springer. Fractales, hasard et finance, 1959–1997, 1 November 1998 Multifractals and 1/ƒ Noise: Wild Self-Affinity in Physics (1963–1976) (Selecta; V...

S2CID 231719831. Hassan, M. K.; Rahman, M. M. (2015). "Percolation on a multifractal scale-free planar stochastic lattice and its universality class". Phys...

analysis. It also has application in related fields such as lacunarity and multifractal analysis. Theoretically, the intent of box counting is to quantify fractal...

ISBN 978-0-521-57066-4. Meneveau, C.; Sreenivasan, K.R. (1991). "The multifractal nature of turbulent energy dissipation". J. Fluid Mech. 224: 429–484...

manifest local variations in fractal dimension, they are said to be multifractals. Examples of data sequences that exhibit local variations in p like...

Gosper curve Pythagoras tree Weierstrass function Strange attractor Multifractal system L-system Fractal canopy Space-filling curve H tree Escape-time...

and econometrics. He pioneered with Adlai Fisher the Markov switching multifractal model of financial volatility, which is used by academics and financial...

method for real option valuation Single-index model Markov switching multifractal Multiple factor models Damodaran, Aswath (31 January 2002). Investment...

speech recognition, acoustics, vibration signals, computer graphics, multifractal analysis, and sparse coding. In computer vision and image processing...

Multifractal Rescaled range Analysis on fractals Gerges, Firas; Geng, Xiaolong; Nassif, Hani; Boufadel, Michel C. (2021). "Anisotropic Multifractal Scaling...

illustrate time dependence at multiple scales. See also Markov switching multifractal (MSMF) techniques for modeling volatility evolution. A hidden Markov...