3 The “Fokker-Planck” equation is a partial differential equation that controls the evolution of the forward (and backward) probabilities 9 3.1 Deriving the “free” Fokker-Planck equation (no spike observations) . . . . . . 10 3.1.1 Conductance-based model . . . . . . . . . . . . . . . . . . . . . . . . . 12 3.1.2 Computing mean firing rates in a network of GLM neurons . . . . . . 13 3.2 Incorpo...

We present a master equation formulation based on a Markovian random walk model that exhibits subdiffusion, classical diffusion, and superdiffusion as a function of a single parameter. The nonclassical diffusive behavior is generated by allowing for interactions between a population of walkers. At the macroscopic level, this gives rise to a nonlinear Fokker-Planck equation. The diffusive behavi...

The determination of the relaxation of electrons in atomic gases continues to be an important physical problem. The main interest is the determination of the time scale for the thermalization of electrons in different moderators and the nature of the time-dependent electron energy distribution. The theoretical basis for the study of electron thermalization is the determination of the electron d...

The exact solution of the Cauchy problem for a generalized ”linear” vectorial Fokker-Planck equation is found using the disentangling techniques of R. Feynman and algebraic (operational) methods. This approach may be considered as a generalization of the Masuo Suzuki’s method for solving the 1-dimensional linear Fokker-Planck equation.

We discuss the approach to equilibrium of systems governed by the Fokker-Planck equation. In particular, we focus on problems involving barrier penetration and the associated Kramers’ time. We also describe the connection between stochastic processes and quantum mechanics. Keywards: Fokker-Planck equation; Approach to equilibrium; Barrier penetration