Steady dynamics of coupled conductance-based integrate-and-fire neuronal networks in the limit of small fluctuations is studied via the equilibrium states of a Fokker-Planck equation. An asymptotic approximation for the membrane-potential probability density function is derived and the corresponding gain curves are found. Validity conditions are discussed for the Fokker-Planck description and v...

We introduce a stochastic particle system that corresponds to the Fokker–Planck equation with decay in the many-particle limit, and study its large deviations. We show that the large-deviation rate functional corresponds to an energy-dissipation functional in a Mosco-convergence sense. Moreover, we prove that the resulting functional, which involves entropic terms and the Wasserstein metric, is...

We describe quantum-field-theoretical (QFT) techniques for mapping quantum problems onto c-number stochastic problems. This approach yields results which are identical to phase-space techniques [C.W. Gardiner, Quantum Noise (1991)] when the latter result in a Fokker-Planck equation for a corresponding pseudo-probability distribution. If phase-space techniques do not result in a Fokker-Planck eq...

Biological tissue scatters light mainly in the forward direction where the scattering phase function has a narrow peak. This peak makes it difficult to solve the radiative transport equation. However, it is just for forward-peaked scattering that the Fokker-Planck equation provides a good approximation, and it is easier to solve than the transport equation. Furthermore, the modification of the ...

In this paper we study the large time behavior for the viscous Burgers’ equation with initial data in L(R). In particular, after a time dependent scaling, we provide the optimal rate of convergence in relative entropy and Wasserstein metric, towards an equilibrium state corresponding to a positive diffusive wave. The main tool in our analysis is the reduction of the rescaled Burgers’ equation t...

We derive, from first principle, the Fokker-Planck equation describing the non-perturbative real-time evolution of a gauge field at high temperatures on the spatial scale (g 2 T) −1 and the time scale (g 4 T) −1 , where g is the gauge coupling and T is the temperature. The knowledge of the effective dynamics on such spatial and time scales is crucial for the understanding and quantitative calcu...

An application of fractional Brownian motion (fBm) is considered in stochastic financial engineering models. For the known Fokker–Planck equation for fBm case, a solution transition probability density path integral method was built. It shown that mentioned does not result from Gaussian unit with precise covariance. expression approximation covariance found which solutions are based on measure ...

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 consider Hamilton–Jacobi equations which characterize optimal controlled partial differential equations of the following types: the Allen–Cahn equation, the Cahn–Hilliard equation, a nonlinear Fokker–Planck equation, and aVlasov–Fokker–Planck equation. In each of the examples, the optimal control problem and its associated cost functional can be derived as limit from a microscopically define...

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...