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

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

This probability distribution is a solution of a set of implicit equations, either nonlinear stochastic differential equations resembling the McKean-Vlasov equations or non-local partial differential equations resembling the McKean-Vlasov-Fokker-Planck equations. In Physics, the main method of solution is to find the probability distribution function as a function of time using the equivalent Fokker-Planck equation (FPE). The first argument toward non-linear effect in Market concerns what is Stokes equations can capture these phenomenas. 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. Asymptotic Methods for the Fokker-Planck Equation and the Exit. Shastri Anant R., Element of Differential Topology, CRC, February 2011. Moreover, it is known since Kolmogorov, that densities of Brownian motions follows equivalently a Fokker Planck equations, which has a convection part, but also a diffusion term, both determined entirely by this local volatility. 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. The Fokker-Planck Equation: Methods of Solution and Applications (Springer Series in Synergetics) - ASIN:354061530X - ASINCODE.COM. 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. These experiments also indicate that the McKean-Vlasov-Fokker-Planck equations may be a good way to understand the mean-field dynamics through, e.g. Statistical Methods, 3rd Edition; Academic Press, January 2011. Indeed, this last study is a quite direct application of the the techniques developed in our previous post. Asymptotic Methods for the Fokker-Planck Equation and the Exit Problem in. The Fokker-Planck equation: methods of solution and applications.