Related papers: A novel numerical method for mean field stochastic…
A numerical solution to the Fokker-Planck equation using a two-level scheme is presented. The Fokker-Planck (FP) equation is of parabolic type equation govern the time evolution of probability density function of the stochastic processes.…
We investigate the stochastic modified equation which plays an important role in the stochastic backward error analysis for explaining the mathematical mechanism of a numerical method. The contribution of this paper is threefold. First, we…
In this paper, we consider the density estimation problem associated with the stationary measure of ergodic It\^o diffusions from a discrete-time series that approximate the solutions of the stochastic differential equations. To take an…
A common issue in simulating geometric evolution of surfaces is unexpected clustering of points that may cause numerical instability. We propose a novel artificial tangential velocity method for this matter. The artificial tangential…
Multivariate global polynomial approximations - such as polynomial chaos or stochastic collocation methods - are now in widespread use for sensitivity analysis and uncertainty quantification. The pseudospectral variety of these methods uses…
We study mean field games with unbounded coefficients. The existence of a solution is proved. We propose a new approach based on Fokker-Planck-Kolmogorov equations, the Ambrosio-Figalli-Trevisan superposition principle, the method of…
In this article we propose a new, explicit and easily implementable numerical method for approximating a class of semilinear stochastic evolution equations with non-globally Lipschitz continuous nonlinearities. We establish strong…
We present new algorithms and fast implementations to find efficient approximations for modelling stochastic processes. For many numerical computations it is essential to develop finite approximations for stochastic processes. While the…
The purpose of this work is to provide a finite dimensional approximation of the solution to a mean field optimal control problem set on the $d$-dimensional torus. The approximation is obtained by means of a Fourier-Galerkin method, the…
The Fokker-Planck (FP) equation governing the evolution of the probability density function (PDF) is applicable to many disciplines but it requires specification of the coefficients for each case, which can be functions of space-time and…
We consider a stochastic heat equation with nonlinear finite-rank space-coloured multiplicative noise that admits a unique nonnegative solution when given nonnegative initial data. Inspired by existing results for fully discrete finite…
We introduce a finite-volume numerical scheme for solving stochastic gradient-flow equations. Such equations are of crucial importance within the framework of fluctuating hydrodynamics and dynamic density functional theory. Our proposed…
In this work, we consider the discretization of some nonlinear Fokker-Planck-Kolmogorov equations. The scheme we propose preserves the non-negativity of the solution, conserves the mass and, as the discretization parameters tend to zero,…
In this paper we study a second-order mean-field stochastic differential systems describing the movement of a particle under the influence of a time-dependent force, a friction, a mean-field interaction and a space and time-dependent…
We develop and analyze a method, density tracking by quadrature (DTQ), to compute the probability density function of the solution of a stochastic differential equation. The derivation of the method begins with the discretization in time of…
A notion of stochastic deformation is introduced and the corresponding algebraic deformation procedure is developed. This procedure is analogous to the deformation of an algebra of observables like deformation quantization, but for an…
The aim of this paper is to develop a general method for constructing approximation schemes for viscosity solutions of fully nonlinear pathwise stochastic partial differential equations, and for proving their convergence. Our results apply…
In this paper, we propose a low rank approximation method for efficiently solving stochastic partial differential equations. Specifically, our method utilizes a novel low rank approximation of the stiffness matrices, which can significantly…
We study a high-dimensional stochastic optimization problem which features both control and stopping. In particular, a central planner steers a large population of particles, and can also remove particles at any time by paying a penalty. In…
We propose and analyze a mixed finite element method for the spatial approximation of a time-fractional Fokker--Planck equation in a convex polyhedral domain, where the given driving force is a function of space. Taking into account the…