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

• Authors: Guy Jumarie
• Languages of publication: EN

Abstracts

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.

Keywords

EN

fractional Gaussian noise; fractional Poissonian noise; fractional partial differential equation; fractional Fokker Planck equation; fractional stochastic differential equations

Discipline

• 05.45.Df: Fractals(see also 47.53.+n Fractals in fluid dynamics; 61.43.Hv Fractals; macroscopic aggregates in structure of solids)
• 05.40.Jc: Brownian motion
• 02.50.Ey: Stochastic processes
• 02.60.Lj: Ordinary and partial differential equations; boundary value problems
• 05.10.Gg: Stochastic analysis methods (Fokker-Planck, Langevin, etc.)

• Publisher: De Gruyter Open
• Journal: Open Physics
• Year: 2008
• Volume: 6
• Issue: 3
• Pages: 737-753

Dates

published

1 - 9 - 2008

online

17 - 7 - 2008

Contributors

author

Guy Jumarie

• Department of Mathematics, University of Québec at Montréal, P.O. Box 8888, Downtown Station, Montréal, Qc H3C 3P8, Canada

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Identifiers

DOI

10.2478/s11534-008-0090-5