Generalized Fokker-Planck equation: Derivation and exact solutions
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چکیده
منابع مشابه
Generalized Fokker-Planck equation: Derivation and exact solutions
We derive the generalized Fokker-Planck equation associated with the Langevin equation (in the Ito sense) for an overdamped particle in an external potential driven by multiplicative noise with an arbitrary distribution of the increments of the noise generating process. We explicitly consider this equation for various specific types of noises, including Poisson white noise and Lévy stable noise...
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In 1984, H. Risken authored a book (H. Risken, The Fokker-Planck Equation: Methods of Solution, Applications, Springer-Verlag, Berlin, New York) discussing the Fokker-Planck equation for one variable, several variables, methods of solution and its applications, especially dealing with laser statistics. There has been a considerable progress on the topic as well as the topic has received greater...
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The Langevin equation approach to the evolution of the velocity distribution for the Brownian particle might leave you uncomfortable. A more formal treatment of this type of problem is given by the Fokker-Planck equation. We can either formulate the question in terms of the evolution of a nonstationary probability distribution from a defined initial condition, or in terms of the evolution of th...
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Microscopic theory of Brownian motion of a particle of mass M in a bath of molecules of mass m<<M is considered beyond lowest order in the mass ratio mM . The corresponding Langevin equation contains nonlinear corrections to the dissipative force, and the generalized Fokker-Planck equation involves derivatives of order higher than 2. These equations are derived from first principles with coeffi...
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ژورنال
عنوان ژورنال: The European Physical Journal B
سال: 2009
ISSN: 1434-6028,1434-6036
DOI: 10.1140/epjb/e2009-00126-3