Related papers: On the approximation of the probability density fu…
We derive a simple and precise approximation to probability density functions in sampling distributions based on the Fourier cosine series. After clarifying the required conditions, we illustrate the approximation on two examples: the…
In this paper, we develop an efficient numerical solver for unsteady diffusion-type partial differential equations with random coefficients. A major computational challenge in such problems lies in repeatedly handling large-scale linear…
Diffusions are a successful technique to sample from high-dimensional distributions. The target distribution can be either explicitly given or learnt from a collection of samples. They implement a diffusion process whose endpoint is a…
The notion of probability density for a random function is not as straightforward as in finite-dimensional cases. While a probability density function generally does not exist for functional data, we show that it is possible to develop the…
Consider a multidimensional diffusion process $X=\{X\left(t\right) :t\in\lbrack0,1]\}$. Let $\varepsilon>0$ be a \textit{deterministic}, user defined, tolerance error parameter. Under standard regularity conditions on the drift and…
We address an original approach for the convergence analysis of a finite-volume scheme for the approximation of a stochastic diffusion-convection equation with multiplicative noise in a bounded domain of $\mathbb{R}^d$ (with $d=2$ or $3$)…
We show how the Stefan type free boundary problem with random diffusion in one space dimension can be approximated by the corresponding free boundary problem with nonlocal diffusion. The approximation problem is a slightly modified version…
We study a general class of singular degenerate parabolic stochastic partial differential equations (SPDEs) which include, in particular, the stochastic porous medium equations and the stochastic fast diffusion equation. We propose a fully…
This paper presents a new numerical scheme for simulating stochastic processes specified by their marginal distribution functions and covariance functions. Stochastic samples are firstly generated to automatically satisfy target marginal…
In the present paper we propose a new stochastic diffusion process with drift proportional to the Weibull density function defined as X $\epsilon$ = x, dX t = $\gamma$ t (1 - t $\gamma$+1) - t $\gamma$ X t dt + $\sigma$X t dB t , t…
In this paper, we propose stochastic structure-preserving schemes to compute the effective diffusivity for particles moving in random flows. We first introduce the motion of particles using the Lagrangian formulation, which is modeled by…
We derive the hydrodynamic limit of a kinetic equation with a stochastic, short range perturbation of the velocity operator. Under some mixing hypotheses on the stochastic perturbation, we establish a diffusion-approximation result: the…
We propose a method for the approximation of solutions of PDEs with stochastic coefficients based on the direct, i.e., non-adapted, sampling of solutions. This sampling can be done by using any legacy code for the deterministic problem as a…
The non-smooth finite-sum minimization is a fundamental problem in machine learning. This paper develops a distributed stochastic proximal-gradient algorithm with random reshuffling to solve the finite-sum minimization over time-varying…
Increasingly larger data sets of processes in space and time ask for statistical models and methods that can cope with such data. We show that the solution of a stochastic advection-diffusion partial differential equation provides a…
We propose a new Neural Galerkin Normalizing Flow framework to approximate the transition probability density function of a diffusion process by solving the corresponding Fokker-Planck equation with an atomic initial distribution,…
We present a Bayesian non-parametric way of inferring stochastic differential equations for both regression tasks and continuous-time dynamical modelling. The work has high emphasis on the stochastic part of the differential equation, also…
In this paper we present an asymptotically compatible meshfree method for solving nonlocal equations with random coefficients, describing diffusion in heterogeneous media. In particular, the random diffusivity coefficient is described by a…
We consider a process given as the solution of a one-dimensional stochastic differential equation with irregular, path dependent and time-inhomogeneous drift coefficient and additive noise. H\"older continuity of the Lebesgue density of…
We consider the one-dimensional diffusion of a particle on a semi-infinite line and in a piecewise linear random potential. We first present a new formalism which yields an analytical expression for the Green function of the Fokker-Planck…