On the derivation of the Fokker-Plank equation by using of Fractional calculus

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Abstract

In this paper, fractional calculus has been used to find the spectral counterpart of the Fokker-Planck equations for non-linear systems driven by Lévy white noise processes. In particular it is shown thatone can obtain the equation ruling the characteristic function of the response to a non-linear system, withoutusing the Itô formula. Indeed, it is possible to reproduce the well-known results, already known in literature,by means of the characteristic function representation in terms of complex moments, recently proposed by thefirst two authors. The case of a-stable Lévy driven stochastic differential equation is also treated introducingan associated process constructed from the stable one.
Lingua originaleEnglish
Pagine965-971
Numero di pagine7
Stato di pubblicazionePublished - 2009

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Fractional Calculus
Characteristic Function
Nonlinear Systems
Fokker-Planck Equation
White noise
Stochastic Equations
Differential equation
Moment

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title = "On the derivation of the Fokker-Plank equation by using of Fractional calculus",
abstract = "In this paper, fractional calculus has been used to find the spectral counterpart of the Fokker-Planck equations for non-linear systems driven by L{\'e}vy white noise processes. In particular it is shown thatone can obtain the equation ruling the characteristic function of the response to a non-linear system, withoutusing the It{\^o} formula. Indeed, it is possible to reproduce the well-known results, already known in literature,by means of the characteristic function representation in terms of complex moments, recently proposed by thefirst two authors. The case of a-stable L{\'e}vy driven stochastic differential equation is also treated introducingan associated process constructed from the stable one.",
keywords = "Fokker-Planck Equations, Fractional Calculus, Random Vibrations",
author = "{Di Paola}, Mario and Giulio Cottone",
year = "2009",
language = "English",
pages = "965--971",

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T1 - On the derivation of the Fokker-Plank equation by using of Fractional calculus

AU - Di Paola, Mario

AU - Cottone, Giulio

PY - 2009

Y1 - 2009

N2 - In this paper, fractional calculus has been used to find the spectral counterpart of the Fokker-Planck equations for non-linear systems driven by Lévy white noise processes. In particular it is shown thatone can obtain the equation ruling the characteristic function of the response to a non-linear system, withoutusing the Itô formula. Indeed, it is possible to reproduce the well-known results, already known in literature,by means of the characteristic function representation in terms of complex moments, recently proposed by thefirst two authors. The case of a-stable Lévy driven stochastic differential equation is also treated introducingan associated process constructed from the stable one.

AB - In this paper, fractional calculus has been used to find the spectral counterpart of the Fokker-Planck equations for non-linear systems driven by Lévy white noise processes. In particular it is shown thatone can obtain the equation ruling the characteristic function of the response to a non-linear system, withoutusing the Itô formula. Indeed, it is possible to reproduce the well-known results, already known in literature,by means of the characteristic function representation in terms of complex moments, recently proposed by thefirst two authors. The case of a-stable Lévy driven stochastic differential equation is also treated introducingan associated process constructed from the stable one.

KW - Fokker-Planck Equations

KW - Fractional Calculus

KW - Random Vibrations

UR - http://hdl.handle.net/10447/41536

M3 - Other

SP - 965

EP - 971

ER -