The European Physical Journal B

, Volume 80, Issue 2, pp 167–175 | Cite as

Probability distribution function for systems driven by superheavy-tailed noise

Article

Abstract.

We develop a general approach for studying the cumulative probability distribution function of localized objects (particles) whose dynamics is governed by the first-order Langevin equation driven by superheavy-tailed noise. Solving the corresponding Fokker-Planck equation, we show that due to this noise the distribution function can be divided into two different parts describing the surviving and absorbing states of particles. These states and the role of superheavy-tailed noise are studied in detail using the theory of slowly varying functions.

Keywords

Characteristic Function Scale Function Probability Distribution Function Sample Path Langevin Equation 

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Copyright information

© EDP Sciences, SIF, Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  1. 1.Max-Planck-Institut für Physik komplexer SystemeDresdenGermany
  2. 2.Sumy State UniversitySumyUkraine

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