Distributions derived from non-extensive Tsallis statistics are closely connected with dynamics described by a nonlinear Fokker-Planck equation. The combination shows promise in describing stochastic processes with power-law distributions and superdiffusive dynamics. We investigate intra-day price changes in the S&P500 stock index within this framework by direct analysis and by simulation. We f...

The present note establishes the self-averaging, radiative transfer limit for the twofrequency Wigner distribution for classical waves in random media. Depending on the ratio of the wavelength to the correlation length the limiting equation is either a Boltzmann-like integral equation or a Fokker-Planck-like differential equation in the phase space. The limiting equation is used to estimate thr...

Submitted for the MAR10 Meeting of The American Physical Society Rate description of Fokker-Planck processes with time-periodic parameters PETER TALKNER, Inst of Physics, University of Augsburg — The large time dynamics of periodically driven Fokker-Planck processes possessing several metastable states is investigated. At weak noise the rare transitions between these metastable states can be re...

The diffusion limit of kinetic systems has been subject numerous studies since prominent works Lebowitz et al. [1] and van Kampen [2]. More recently, the topic seen a fresh interest from rarefied gas simulation perspective. In particular, Fokker-Planck based models provide novel approximations Boltzmann equation, where relaxation induced by binary collisions is modeled via continuous stochastic...

We present a class of asymptotic-preserving (AP) schemes for the nonhomogeneous Fokker–Planck–Landau (nFPL) equation. Filbet and Jin [16] designed a class of AP schemes for the classical Boltzmann equation, by penalization with the BGK operator, so they become efficient in the fluid dynamic regime. We generalize their idea to the nFPL equation, with a different penalization operator, the Fokker...

We find a numerical self-consistent stellar model by finding the distribution function of a thin disk that satisfies simultaneously the Fokker-Planck and Poisson equations. The solution of the Fokker-Planck equation is found by a direct numerical solver using finite differences and a variation of Stone’s method. The collision term in the Fokker-Planck equation is found using the local approxima...