Related papers: Ornstein-Uhlenbeck approximation of one-step proce…
Policy gradients methods often achieve better performance when the change in policy is limited to a small Kullback-Leibler divergence. We derive policy gradients where the change in policy is limited to a small Wasserstein distance (or…
We propose a systematic method to derive the asymptotic behaviour of the persistence distribution, for a large class of stochastic processes described by a general Fokker-Planck equation in one dimension. Theoretical predictions are…
The Ornstein-Uhlenbeck process is interpreted as Brownian motion in a harmonic potential. This Gaussian Markov process has a bounded variance and admits a stationary probability distribution, in contrast to the standard Brownian motion. It…
The optimized expansion is used to formulate a systematic approximation scheme to the probability distribution of a stochastic system. The first order approximation for the one-dimensional system driven by noise in an anharmonic potential…
We review some properties of the stationary states of the Fokker - Planck equation for N interacting particles within a mean field approximation, which yields a non-linear integrodifferential equation for the particle density. Analytical…
We design a deterministic particle method for the solution of the spatially homogeneous Landau equation with uncertainty. The deterministic particle approximation is based on the reformulation of the Landau equation as a formal gradient…
A numerical scheme for approximating the nonlinear filtering density is introduced and its convergence rate is established, theoretically under a parabolic H\"{o}rmander condition, and empirically in numerical examples. In a prediction…
We use the Fokker Planck equation as a starting point for studying the orientational probability distribution of an Active Brownian Particle (ABP) in $(d+1)$ dimensions. This Fokker Planck equation admits an exact solution in series form…
We study a class of nonlinear kinetic Fokker-Planck type equations modeling quantum particles which obey the Bose-Einstein and Fermi-Dirac statistics, respectively. We establish the existence of classical solutions in the perturbative…
A pointlike particle of finite mass m, moving in a one-dimensional viscous environment and biased by a spatially dependent force, is considered. We present a rigorous mapping of the Fokker-Planck equation, which determines evolution of the…
Presentation of the probability as an intrinsic property of the nature leads researchers to switch from deterministic to stochastic description of the phenomena. The procedure of stochastization of one-step process was formulated. It allows…
In this paper we study the dynamics of a fast-slow Fokker-Planck partial differential equation (PDE) viewed as the evolution equation for the density of a multiscale planar stochastic differential equation (SDE). Our key focus is on the…
We consider the PDE-constrained optimal control of a leader-follower kinetic opinion formation model, with a Fokker-Planck-type system of partial differential equations as a state constraint. We derive the Boltzmann-type and…
In this work, we consider the solvability of the Fokker-Planck equation with both time-dependent drift and diffusion coefficients by means of the similarity method. By the introduction of the similarity variable, the Fokker-Planck equation…
This paper develops a control and estimation design for the one-phase Stefan problem. The Stefan problem represents a liquid-solid phase transition as time evolution of a temperature profile in a liquid-solid material and its moving…
This article is the exploration of the viewpoint within which propelled particles in a steady-state are regarded as a system with quenched disorder. The analogy is exact when the rate of the drift orientation vanishes and the linear…
We develop the stochastic approach to thermodynamics based on the stochastic dynamics, which can be discrete (master equation) continuous (Fokker-Planck equation), and on two assumptions concerning entropy. The first is the definition of…
In this paper, we study the numerical approximation of a system of PDEs with fractional time derivatives. This system is derived from an optimal control problem for a time-fractional Fokker-Planck equation with time dependent drift by…
We study Markov processes associated with stochastic differential equations, whose non-linearities are gradients of convex functionals. We prove a general result of existence of such Markov processes and a priori estimates on the transition…
In analogy to Brownian computers we explicitly show how to construct stochastic models, which mimic the behaviour of a general purpose computer (a Turing machine). Our models are discrete state systems obeying a Markovian master equation,…