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2008 | 6 | 3 | 737-753
Tytuł artykułu

Generalized Fokker-Planck equation for a class of stochastic dynamical systems driven by additive Gaussian and Poissonian fractional white noises of order α

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Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
In a first stage, the paper deals with the derivation and the solution of the equation of the probability density function of a stochastic system driven simultaneously by a fractional Gaussian white noise and a fractional Poissonian white noise both of the same order. The key is the Taylor’s series of fractional order f(x + h) = E α(hαDx α)f(x) where E α() denotes the Mittag-Leffler function, and D x α is the so-called modified Riemann-Liouville fractional derivative which removes the effects of the non-zero initial value of the function under consideration. The corresponding fractional linear partial differential equation is solved by using a suitable extension of the Lagrange’s technique involving an auxiliary set of fractional differential equations. As an example, one considers a half-oscillator of fractional order driven by a fractional Poissonian noise.
Wydawca

Czasopismo
Rocznik
Tom
6
Numer
3
Strony
737-753
Opis fizyczny
Daty
wydano
2008-09-01
online
2008-07-17
Twórcy
autor
  • Department of Mathematics, University of Québec at Montréal, P.O. Box 8888, Downtown Station, Montréal, Qc H3C 3P8, Canada
Bibliografia
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Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.-psjd-doi-10_2478_s11534-008-0090-5
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