منابع مشابه
The Fokker-Planck equation
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...
متن کاملThe Fokker-Planck Equation
Stochastic differential equations (SDE) are used to model many situations including population dynamics, protein kinetics, turbulence, finance, and engineering [5, 6, 1]. Knowing the solution of the SDE in question leads to interesting analysis of the trajectories. Most SDE are unsolvable analytically and other methods must be used to analyze properties of the stochastic process. From the SDE, ...
متن کاملFokker-Planck Equation
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...
متن کاملExtension of Eigenfunction-expansion Solutions of a Fokker-planck Equation-i. First Order System
Ah&met-The work is concerned with eigenfunction-expItnsion solutions to the forward FokkerPlanck equation associated with a specific, non-linear, first-order system subject to white noise excitation. Using a digital computer, a substantial number of new terms in the expansions have been generated. With this new information, inverted Domb-Sykes plots revealed a pattern in the coefficients for ce...
متن کاملParameters of the fractional Fokker-Planck equation
We study the connection between the parameters of the fractional Fokker-Planck equation, which is associated with the overdamped Langevin equation driven by noise with heavytailed increments, and the transition probability density of the noise generating process. Explicit expressions for these parameters are derived both for finite and infinite variance of the rescaled transition probability de...
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ژورنال
عنوان ژورنال: Proceedings of the Japan Academy, Series A, Mathematical Sciences
سال: 1949
ISSN: 0386-2194
DOI: 10.3792/pja/1195571867