Related papers: Approximation analysis for weak solutions of stoch…
In this paper, we provide a theoretical analysis of the recently introduced weakly adversarial networks (WAN) method, used to approximate partial differential equations in high dimensions. We address the existence and stability of the…
In this paper we prove the existence of global weak dissipative martingale solutions for a one-dimensional compressible fluid model with capillarity and density dependent viscosity, driven by random initial data and a stochastic forcing…
This paper presents a finite-dimensional approximation for a class of partial differential equations on the space of probability measures. These equations are satisfied in the sense of viscosity solutions. The main result states the…
A class of stochastic parabolic equations with singular potentials is analysed in the chaos expansion setting where the Wick product is used to give sense to the product of generalized stochastic processes. For the analysis of such…
Calibration of large-scale differential equation models to observational or experimental data is a widespread challenge throughout applied sciences and engineering. A crucial bottleneck in state-of-the art calibration methods is 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…
Numerical approximation of a stochastic partial integro-differential equation driven by a space- time white noise is studied by truncating a series representation of the noise, with finite element method for spatial discretization and…
The Wigner function of quantum systems is an effective instrument to construct the approximate classical description of the systems for which the classical approximation is possible. During the last time, the Wigner function formalism is…
We consider a finite element approximation of a general semi-linear stochastic partial differential equation (SPDE) driven by space-time multiplicative and additive noise. We examine the full weak convergence rate of the exponential Euler…
An averaging method is applied to derive effective approximation to the following singularly perturbed nonlinear stochastic damped wave equation \nu u_{tt}+u_t=\D u+f(u)+\nu^\alpha\dot{W} on an open bounded domain $D\subset\R^n$\,, $1\leq…
In this paper parabolic random partial differential equations and parabolic stochastic partial differential equations driven by a Wiener process are considered. A deterministic, tensorized evolution equation for the second moment and the…
This work is concerned with a singularly perturbed stochastic nonlinear wave equation with a random dynamical boundary condition. A splitting skill is used to derive the approximating equation of the system in the sense of probability…
According to Talay and Tubaro \cite{talay_expansion_1990}, the weak error between the solution to a stochastic differential equation with smooth coefficients and its Euler-Maruyama scheme can be expanded in powers of the time-step. In the…
In this paper we prove an approximation result for the viscosity solution of a system of semi-linear partial differential equations with continuous coefficients and nonlinear Neumann boundary condition. The approximation we use is based on…
Stochastic approximation techniques have been used in various contexts in data science. We propose a stochastic version of the forward-backward algorithm for minimizing the sum of two convex functions, one of which is not necessarily…
Diffusion approximation provides weak approximation for stochastic gradient descent algorithms in a finite time horizon. In this paper, we introduce new tools motivated by the backward error analysis of numerical stochastic differential…
We introduce a new class of fractional backward orthogonal functions designed for the spectral approximation of weakly singular adjoint Volterra integral equations. These basis functions generate an approximation space that naturally…
It is known that when the diffuse interface thickness $\epsilon$ vanishes, the sharp interface limit of the stochastic reaction-diffusion equation is formally a stochastic geometric flow. To capture and simulate such geometric flow, it is…
Recent work on Path-Dependent Partial Differential Equations (PPDEs) has shown that PPDE solutions can be approximated by a probabilistic representation, implemented in the literature by the estimation of conditional expectations using…
We study a class of stochastic evolution equations in a Banach space $E$ driven by cylindrical Wiener process. Three different concept of solutions: generalised strong, weak and mild are defined and the conditions under which they are…