Journal ArticleDOI
Calcul des Probabilités. By Paul Lévy. Pp. 350. Fr. 40. 1925. (Gauthier-Villars.)
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This article is published in The Mathematical Gazette.The article was published on 1926-10-01. It has received 527 citations till now.read more
Citations
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The random walk's guide to anomalous diffusion: a fractional dynamics approach
Ralf Metzler,Joseph Klafter +1 more
TL;DR: Fractional kinetic equations of the diffusion, diffusion-advection, and Fokker-Planck type are presented as a useful approach for the description of transport dynamics in complex systems which are governed by anomalous diffusion and non-exponential relaxation patterns.
Journal ArticleDOI
A subordinated stochastic process model with finite variance for speculative prices
TL;DR: In this article, a general class of finite-variance distributions for price changes is described, and a member of this class, the lognormal-normal, is tested against previously proposed distributions for speculative price differences.
Journal ArticleDOI
A Riemannian Framework for Tensor Computing
TL;DR: This paper proposes to endow the tensor space with an affine-invariant Riemannian metric and demonstrates that it leads to strong theoretical properties: the cone of positive definite symmetric matrices is replaced by a regular and complete manifold without boundaries, the geodesic between two tensors and the mean of a set of tensors are uniquely defined.
Journal ArticleDOI
Detecting long-range correlations with detrended fluctuation analysis
TL;DR: It is shown that deviations from scaling which appear at small time scales become stronger in higher orders of detrended fluctuation analysis, and a modified DFA method is suggested to remove them.
Journal ArticleDOI
Über die analytischen Methoden in der Wahrscheinlichkeitsrechnung
TL;DR: In this paper, a Physikalischer Prozes (die Anderung eines physikalischen systems) heist stochastisch-definit, wenn aus der Kenntnis des ZustandesX0 des Systems in einem gewissen Zeitmomentt0 die verteilungsfunktion der Wahrscheinlichkeiten fur die moglichen ZustandeX des systems in ainem Zeitmomentsumt>t0 folgt.
References
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Journal ArticleDOI
The random walk's guide to anomalous diffusion: a fractional dynamics approach
Ralf Metzler,Joseph Klafter +1 more
TL;DR: Fractional kinetic equations of the diffusion, diffusion-advection, and Fokker-Planck type are presented as a useful approach for the description of transport dynamics in complex systems which are governed by anomalous diffusion and non-exponential relaxation patterns.
Journal ArticleDOI
A subordinated stochastic process model with finite variance for speculative prices
TL;DR: In this article, a general class of finite-variance distributions for price changes is described, and a member of this class, the lognormal-normal, is tested against previously proposed distributions for speculative price differences.
Book
Introduction to Econophysics: Correlations and Complexity in Finance
TL;DR: Economists and workers in the financial world will find useful the presentation of empirical analysis methods and well-formulated theoretical tools that might help describe systems composed of a huge number of interacting subsystems.
Journal ArticleDOI
A Riemannian Framework for Tensor Computing
TL;DR: This paper proposes to endow the tensor space with an affine-invariant Riemannian metric and demonstrates that it leads to strong theoretical properties: the cone of positive definite symmetric matrices is replaced by a regular and complete manifold without boundaries, the geodesic between two tensors and the mean of a set of tensors are uniquely defined.
Journal ArticleDOI
Detecting long-range correlations with detrended fluctuation analysis
TL;DR: It is shown that deviations from scaling which appear at small time scales become stronger in higher orders of detrended fluctuation analysis, and a modified DFA method is suggested to remove them.