Related papers: Using Malliavin calculus to solve a chemical diffu…
We extend the Langevin approach to a class of driving noises whose generating processes have independent increments with super-heavy-tailed distributions. The time-dependent generalized Fokker-Planck equation that corresponds to the…
Inspired by the stochastic particle method, this paper establishes an easily implementable explicit numerical method for McKean-Vlasov stochastic differential equations (MV-SDEs) with superlinear growth coefficients. The paper establishes…
Basic derivative formulas are presented for hypoelliptic heat semigroups and harmonic functions extending earlier work in the elliptic case. Emphasis is placed on developing integration by parts formulas at the level of local martingales.…
We present a finite element approach for diffusion problems with thermal fluctuations based on a fluctuating hydrodynamics model. The governing transport equations are stochastic partial differential equations with a fluctuating forcing…
We study the "one and one-half" dimensional Vlasov-Maxwell-Fokker-Planck system and obtain the first results concerning well-posedness of solutions. Specifically, we prove the global-in-time existence and uniqueness in the large of…
In this paper, we obtain the existence and finite-time blow-up for the solution to a system of semilinear stochastic partial differential equations driven by a combination of Brownian and fractional Brownian motions. Under suitable…
In this paper we analyze fractional Fokker-Planck equation describing subdiffusion in the general infinitely divisible (ID) setting. We show that in the case of space-time-dependent drift and diffusion and time-dependent jump coefficient,…
A generalized Langevin equation is suggested to describe a system with memory($u(t,t') = \frac{1}{\Gamma (\nu )}(t - t')^\nu $) as well as with positive and negative damping. The equation can be transformed into the Fokker-Planck equation…
A new simple Lagrangian method with favorable stability and efficiency properties for computing general plane curve evolutions is presented. The method is based on the flowing finite volume discretization of the intrinsic partial…
In this paper, we develop and analyze numerical methods for high dimensional Fokker-Planck equations by leveraging generative models from deep learning. Our starting point is a formulation of the Fokker-Planck equation as a system of…
Stochastic optimal control problems with constraints on the probability distribution of the final output are considered. Necessary conditions for optimality in the form of a coupled system of partial differential equations involving a…
Initiated around the year 2007, the Malliavin-Stein approach to probabilistic approximations combines Stein's method with infinite-dimensional integration by parts formulae based on the use of Malliavin-type operators. In the last decade,…
We propose a novel approach for modeling chemical reactions within the particle-based Fokker-Planck framework for gas flow simulations which conserves mass, momentum, and energy while retaining the performance advantages of the…
A fundamental problem in Bayesian inference and statistical machine learning is to efficiently sample from multimodal distributions. Due to metastability, multimodal distributions are difficult to sample using standard Markov chain Monte…
We study an approximation scheme based on a second quantization method for a chemical master equation. Small systems, such as cells, could not be studied by the traditional rate equation approach because fluctuation effects are very large…
The purpose of this paper is to study optimal control of conditional McKean-Vlasov (mean-field) stochastic differential equations with jumps (conditional McKean-Vlasov jump diffusions, for short). To this end, we first prove a stochastic…
The Fokker--Planck equation is a key ingredient of many models in physics, and related subjects, and arises in a diverse array of settings. Analytical solutions are limited to special cases, and resorting to numerical simulation is often…
The present work provides a critical assessment of numerical solutions of the space-fractional diffusion-advection equation, which is of high significance for applications in various natural sciences. In view of the fact that, in contrast…
The Fokker-Planck equation describes the evolution of the probability density associated with a stochastic differential equation. As the dimension of the system grows, solving this partial differential equation (PDE) using conventional…
Generalising the work of Lenard and Bernstein, we introduce a new, fully relativistic model to describe collisional plasmas. Like the Fokker-Planck operator, this equation represents velocity diffusion and conserves particle number.…