The present paper establishes the self-averaging, radiative transfer limit for the twofrequency Wigner distribution for random classical waves in the paraxial approximation. Depending on the ratio of the wavelength to the correlation length the limiting equation is either a Boltzmannlike integral equation or a Fokker-Planck-like differential equation in the phase space. When the longitudinal fl...

We study mixed-moment models (full zeroth moment, half higher moments) for a Fokker–Planck equation in one space dimension. Mixed-moment minimum-entropy models are known to overcome the zero net-flux problem of full-moment minimum-entropy Mn models. A realizability theory for these mixed moments of arbitrary order is derived, as well as a new closure, which we refer to as Kershaw closure. They ...

— We investigate the non cut-off Kac équation when the cross-section is concentrating on grazing collisions. We prove that this process leads to the one-dimensional Fokker-Planck équation, and that, at last under suitable regularity of the initial data, the convergence is uniform in time. © Elsevier, Paris Résumé. — On s'intéresse à l'équation de Kac « non cut-off» lorsque la section transversa...

We study the approximation of Wasserstein gradient structures by their finitedimensional analog. We show that simple finite-volume discretizations of the linear Fokker-Planck equation exhibit the recently established entropic gradient-flow structure for reversible Markov chains. Then we reprove the convergence of the discrete scheme in the limit of vanishing mesh size using only the involved gr...

Abstract. We investigate linear Fokker-Planck equations or stochastic Hamiltonian systems with periodic forcing where the impact of deterministic forcing is not captured by classical stochastic averaging. To overcome this problem, a formal energy projection method is introduced, which splits the corresponding Fokker-Planck equation and allows the computation of higher order stochastic averages....

By considering an ensemble of Brownian particles suspended in a heat bath as a thermodynamic system with an internal degree of freedom it is possible to obtain the Fokker-Planck equation for Brownian motion in a temperature gradient, by applying the scheme of non-equilibrium thermodynamics. We recover explicitely the equations derived in particular by Zubarev and Bashkirov using statistical mec...

We present a generalization of Zwanzig's method of projection operators to the case where the underlying dynamics is not deterministic. The method allows us to perform a coarse graining of an already coarse-grained level of description in which fluctuations are important. The initial level of description is described by a Fokker-Planck equation and, under suitable approximations, the final slow...