相关论文: Optimal convergence rates in the averaging princip…

In this paper, we study the numerical approximation of a general second order semilinear stochastic partial differential equation (SPDE) driven by a additive fractional Brownian motion (fBm) with Hurst parameter $H>\frac 12$ and Poisson…

The strong numerical approximation of semilinear stochastic partial differential equations (SPDEs) driven by infinite dimensional Wiener processes is investigated. There are a number of results in the literature that show that Euler-type…

Recently, in a paper by Jentzen and Kloeden [Proc. R. Soc. Lond. Ser. A Math. Phys. Eng. Sci. 465 (2009) 649-667], a new method for simulating nearly linear stochastic partial differential equations (SPDEs) with additive noise has been…

This paper develops and analyzes a fully discrete finite element method for a class of semilinear stochastic partial differential equations (SPDEs) with multiplicative noise. The nonlinearity in the diffusion term of the SPDEs is assumed to…

This paper introduces SPDE bridges with observation noise and contains an analysis of their spatially semidiscrete approximations. The SPDEs are considered in the form of mild solutions in an abstract Hilbert space framework suitable for…

In this work, we provide the first strong convergence result of numerical approximation of a general second order semilinear stochastic fractional order evolution equation involving a Caputo derivative in time of order $\alpha\in(\frac 34,…

We consider a quasilinear parabolic stochastic partial differential equation driven by a multiplicative noise and study regularity properties of its weak solution satisfying classical a priori estimates. In particular, we determine…

In this work, we study a class of non-autonomous two-time-scale stochastic reaction-diffusion equations driven by Poisson random measures, in which the coefficients satisfy the polynomial growth condition and local Lipschitz condition.…

We first establish strong convergence rates for multiscale systems driven by $\alpha$-stable processes, with analyses constructed in two distinct scaling regimes. When addressing weak convergence rates of this system, we derive four…

In this paper, we study the diffusion approximation for slow-fast stochastic differential equations with state-dependent switching, where the slow component $X^{\varepsilon}$ is the solution of a stochastic differential equation with…

The regularity and characterization of solutions to degenerate, quasilinear SPDE is studied. Our results are two-fold: First, we prove regularity results for solutions to certain degenerate, quasilinear SPDE driven by Lipschitz continuous…

We study stochastic partial differential equations (SPDEs) with potentially very rough fractional noise with Hurst parameter $H\in(0,1)$. Close to a change of stability measured with a small parameter $\varepsilon$, we rely on the natural…

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…

In this paper, we study the averaging principle and central limit theorem for multi-scale stochastic differential equations with state-dependent switching. To accomplish this, we first study the Poisson equation associated with a Markov…

In this paper, we study the asymptotic behavior of a semi-linear slow-fast stochastic partial differential equation with singular coefficients. Using the Poisson equation in Hilbert space, we first establish the strong convergence in the…

In this work we establish weak convergence rates for temporal discretisations of stochastic wave equations with multiplicative noise, in particular, for the hyperbolic Anderson model. For this class of stochastic partial differential…

We propose some new mixed finite element methods for the time dependent stochastic Stokes equations with multiplicative noise, which use the Helmholtz decomposition of the driving multiplicative noise. It is known [16] that the pressure…

It is well known that the Euler method for a random ordinary differential equation $\mathrm{d}X_t/\mathrm{d}t = f(t, X_t, Y_t)$ driven by a stochastic process $\{Y_t\}_t$ with $\theta$-H\"older sample paths is estimated to be of strong…

This article proposes and analyzes explicit and easily implementable temporal numerical approximation schemes for additive noise-driven stochastic partial differential equations (SPDEs) with polynomial nonlinearities such as, e.g.,…

The paper studies the well-posedness and optimal error estimates of spectral finite element approximations for the boundary value problems of semi-linear elliptic SPDEs driven by white or colored Gaussian noises. The noise term is…