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Influence of super-extreme events on a Weierstrass-Mandelbrot Continuous-Time Random Walk

Tomasz R. Werner 1Tomasz Gubiec 2Ryszard Kutner 2Didier Sornette 3

1. Uniwersytet Warszawski, Wydział Fizyki, Instytut Fizyki Teoretycznej (IFTUW), Hoża 69, Warszawa 00-681, Poland
2. University of Warsaw, Institute of Experimental Physics (IFDUW), Hoża 69, Warsaw 00-681, Poland
3. ETH Zürich (ETHZ), Wolfgang-Pauli-Strasse 10, Zürich 8093, Switzerland

Abstract

Two key utmost cases of influence of super-extreme events on the velocity autocorrelation function (VAF) were considered. The VAF itself was derived within the hierarchical Weierstrass-Mandelbrot Continuous-Time Random Walk (WM-CTRW) formalism which is able to cover a broad spectrum of continuous-time random walks. Firstly, we studied a super-extreme event in a form of the sustained one, whose duration time is much longer than that of all other events. Secondly, we considered a super-extreme event in the form of a shock with the size and velocity much larger than those corresponding to any other event. We found that the appearance of the super-extreme event substantially changes the resulting VAF; in each case considered, these changes are quite different.

 

Auxiliary resources (full texts, presentations, posters, etc.)
  1. PRESENTATION: Influence of super-extreme events on a Weierstrass-Mandelbrot Continuous-Time Random Walk, PDF document, version 1.4, 1.1MB
 

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Related papers

Presentation: Oral at 5 Ogólnopolskie Sympozjum "Fizyka w Ekonomii i Naukach Społecznych", by Tomasz R. Werner
See On-line Journal of 5 Ogólnopolskie Sympozjum "Fizyka w Ekonomii i Naukach Społecznych"

Submitted: 2010-10-09 17:26
Revised:   2010-10-13 12:44