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The Fokker-Planck equation: methods of solution and applications by H. Risken

The Fokker-Planck equation: methods of solution and applications H. Risken ebook
Page: 485
Format: djvu
ISBN: 0387130985, 9780387130989
Publisher: Springer-Verlag

Nowadays, numerical simulations of plasmas are receiving a great deal of attention both in research and in industry thanks to the numerous applications directly connected to these phenomena. Then, using a non-linear Fokker-Planck equation, one adds a SV component and for any given set of SV parameters computes a new "leveraged local volatility surface" that still matches the vanillas, while accommodating SV. Jumarie, “Probability calculus of fractional order and fractional Taylor's series application to Fokker-Planck equation and information of non-random functions,” Chaos, Solitons and Fractals, vol. Risken: The Fokker–Planck Equation: Methods of Solution and Applications (Springer-Verlag, Berlin, 1996). Diffusion equations on Cantor sets. Risken: The Fokker-Planck Equation: Methods of Solution and Applications (Springer, Berlin, 1989) 2nd ed. Some examples are given to illustrate the efficiency and accuracy of the proposed method to obtain analytical solutions to differential equations within the local fractional derivatives. The method is based upon hybrid function approximate. The SLV Calibrator then applies to this PDE solution a Levenberg-Marquardt optimizer and finds the (time bucketed) SV parameters that yield a maximally flat leveraged local volatility surface. Other techniques, such as path integration have also been used, What is important in this application is that the Fokker–Planck equation can be used for computing the probability densities of stochastic differential equations. In addition, there exist many practical situations in F.Filbet, L.Pareschi, A numerical method for the accurate solution of the Fokker-Planck-Landau equation in the non homogeneous case, Journal of Computational Physics, 179, 1-26 (2002). The Fredholm-type equations, which have many applications in mathematical physics, are then considered. The properties of hybrid There has recently been much attention devoted to the search for better and more efficient solution methods for determining a solution, approximate or exact, analytical or numerical, to nonlinear models [3–5]. The main method of solution is by use of the Fokker-Planck equation (b), which provides a deterministic equation satisfied by the time dependent probability density. A formal analogy of the Fokker–Planck equation with the Schrodinger equation allows the use of advanced operator techniques known from quantum mechanics for its solution in a number of cases.