PUMA
Istituto di Scienza e Tecnologie dell'Informazione     
Paradisi P. Linking fractional calculus to real data. In: FCPNLO 2014 - Fractional Calculus, Probability and Non-local Operators: Applications and Recent Developments. A workshop on the occasion of the retirement of Francesco Mainardi (Bilbao, Spain, 6-8 November 2013).
 
 
Abstract
(English)
I will review some well-known theoretical findings about fractional calculus and, in particular, the links between fractal intermittency, the Continuous Time Random Walk (CTRW) model and the emergence of Fractional Diffu- sion Equations (FDE) for anomalous diffusion. In this framework, I will show how fractional operators are associated with the existence of renewal events, a typical feature of complex systems. I will also discuss the possibile connections with critical phenomena. Then, I will introduce some statistical methods allowing to understand when a real system could be described by means of fractional models. Finally, I will show some applications to real data from nano-crystal fluores- cence intermittency, human brain dynamics and atmospheric turbulence.
URL: http://https://sites.google.com/site/fcpnlo/
Subject Stochastic processes
Renewal processes
Fractional calculus
Anomalous diffusion
Time series analysis
Signal processing
J.2 PHYSICAL SCIENCES AND ENGINEERING
I.4.6 IMAGE PROCESSING AND COMPUTER VISION. Segmentation
I.5.4 PATTERN RECOGNITION. Applications
G.3 PROBABILITY AND STATISTICS
46N55 Applications in statistical physics
47N30 Applications in probability theory and statistics
60-xx Probability theory and stochastic processes
62-xx Statistics


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