相关论文: Weak error analysis for semilinear stochastic Volt…

We consider a numerical approximation of a linear quadratic control problem constrained by the stochastic heat equation with non-homogeneous Neumann boundary conditions. This involves a combination of distributed and boundary control, as…

This paper focuses on deriving optimal-order full moment error estimates in strong norms for both velocity and pressure approximations in the Euler-Maruyama time discretization of the stochastic Navier-Stokes equations with multiplicative…

This work is devoted to studying asymptotic behaviors for Volterra type McKean-Vlasov stochastic differential equations with small noise. By applying the weak convergence approach, we establish the large and moderate deviation principles.…

In astrophysics and meteorology there exist numerous situations where flows exhibit small velocities compared to the sound speed. To overcome the stringent timestep restrictions posed by the predominantly used explicit methods for…

We prove that the implicit time Euler scheme coupled with finite elements space discretization for the 2D Navier-Stokes equations on the torus subject to a random perturbation converges in $L^2(\Omega)$, and describe the rate of convergence…

Approximating the invariant measure and the expectation of the functionals for parabolic stochastic partial differential equations (SPDEs) with non-globally Lipschitz coefficients is an active research area and is far from being well…

We propose a spectral viscosity method (SVM) to approximate the incompressible Euler equations driven by a multiplicative noise. We show that SVM solution converges to a dissipative measure-valued martingale solution. These solutions are…

The convergence of stochastic integrals driven by a sequence of Wiener processes $W_n\to W$ (with convergence in $C_t$) is crucial in the analysis of stochastic partial differential equations (SPDEs). The convergence we focus on in this…

We study a compound Poisson (random time-change) approximation for stochastic differential equations (SDEs) and stochastic Volterra equations whose coefficients may be merely measurable in time and may even exhibit integrable singularities.…

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…

We consider a sparse grid collocation method in conjunction with a time discretization of the differential equations for computing expectations of functionals of solutions to differential equations perturbed by time-dependent white noise.…

We derive stochastic compressible Euler Equation from a Hamiltonian microscopic dynamics. We consider systems of interacting particles with H\"older noise and potential whose range is large in comparison with the typical distance between…

Error estimates are proved for finite element approximations to the solution of second-order hyperbolic partial differential equations with coefficients varying in both space and time. Optimal rates of convergence in the energy norm are…

Unlike many deterministic PDEs, stochastic equations are not amenable to the classical variational theory of Euler-Lagrange. In this paper, we show how self-dual variational calculus leads to solutions of various stochastic partial…

A semilinear initial-boundary value problem with a Caputo time derivative of fractional order $\alpha\in(0,1)$ is considered, solutions of which typically exhibit a singular behaviour at an initial time. For L1-type discretizations of this…

This work investigates a fully discrete mixed finite element method for the stochastic Boussinesq system driven by multiplicative noise. The spatial discretization is performed using a standard mixed finite element method, while the…

In this paper, we first establish the existence, uniqueness and H\"older continuity of the solution to stochastic Volterra integral equations with weakly singular kernels. Then, we propose a $\theta$-Euler-Maruyama scheme and a Milstein…

We consider the stochastic Navier--Stokes equations in three dimensions and prove that the law of analytically weak solutions is not unique. In particular, we focus on three examples of a stochastic perturbation: an additive, a linear…

In this paper, a weak Local Linearization scheme for Stochastic Differential Equations (SDEs) with multiplicative noise is introduced. First, for a time discretization, the solution of the SDE is locally approximated by the solution of the…

A M\"untz spectral collocation method is implemented for solving weakly singular Volterra integro-differential equations (VDIEs) with proportional delays. After constructing the numerical scheme to seek an approximate solution, we derive…