相关论文: Lattice Approximations of Semilinear Stochastic El…
We introduce a discretization/approximation scheme for reflected stochastic partial differential equations driven by space-time white noise through systems of reflecting stochastic differential equations. To establish the convergence of the…
We study a stochastic boundary value problem on $(0,1)^d$ of elliptic type in dimension $d\ge 4$, driven by a coloured noise. An approximation scheme based on a suitable discretization of the Laplacian on a lattice of $(0,1)^d$ is…
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…
In this article, we study elliptic stochastic partial differential equations with two reflect- ing walls h1 and h2, driven by multiplicative noise. The existence and uniqueness of the solutions are established.
In this paper, we study the Wong-Zakai approximation of the solution to the stochastic differential equation on a domain $D$ in a Euclidean space with normal reflection at the boundary. We prove the $L^p$ convergence of the approximation in…
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 numerical approximation of the solution to a stochastic partial differential equation with additive spatial white noise on a bounded domain is considered. The differential operator is assumed to be a fractional power of an integer order…
We consider strong convergence of the finite differences approximation in space for stochastic reaction diffusion equations with multiplicative noise under a one-sided Lipschitz condition only. We derive convergence with an implicit rate…
We study approximations to a class of vector-valued equations of Burgers type driven by a multiplicative space-time white noise. A solution theory for this class of equations has been developed recently in [Hairer, Weber, Probab. Theory…
White noise-driven nonlinear stochastic partial differential equations (SPDEs) of parabolic type are frequently used to model physical and biological systems in space dimensions d = 1,2,3. Whereas existence and uniqueness of weak solutions…
For semilinear stochastic evolution equations whose coefficients are more general than the classical global Lipschitz, we present results on the strong convergence rates of numerical discretizations. The proof of them provides a new…
We consider a stochastic partial differential equation with logarithmic (or negative power) nonlinearity, with one reflection at 0 and with a constraint of conservation of the space average. The equation, driven by the derivative in space…
We study for the first time the Cauchy problem for semilinear fractional elliptic equation. This paper is concerned with the Gaussian white noise model for the initial Cauchy data. We establish the ill-posedness of the problem. Then, under…
Motivated by the simulation of stable random fields, we consider the issue of discrete approximations of independently scattered stable noise. Two approaches are proposed: grid approximations available when the underlying space is $\bbR^d$…
In this paper, we establish the existence and uniqueness of invariant measures for a class of semilinear stochastic partial differential equations driven by multiplicative noise on a bounded domain. The main results can be applied to SPDEs…
In this paper we study approximations to 3D Navier-Stokes (NS) equation driven by space-time white noise by paracontrolled distribution proposed in [GIP13]. A solution theory for this equation has been developed recently in [ZZ14] based on…
We provide convergence rates for space approximations of semi-linear stochastic differential equations with multiplicative noise in a Hilbert space. The space approximations we consider are spectral Galerkin and finite elements, and the…
This article is devoted to the numerical study of various finite difference approximations to the stochastic Burgers equation. Of particular interest in the one-dimensional case is the situation where the driving noise is white both in…
We establish the $L_p$-regularity theory for a semilinear stochastic partial differential equation with multiplicative white noise: $$ du = (a^{ij}u_{x^ix^j} + b^{i}u_{x^i} + cu + \bar b^{i}|u|^\lambda u_{x^i})dt + \sigma^k(u)dw_t^k,\quad…
In this paper, we establish an existence and uniqueness result for system of quasilinear stochastic partial differential equations (SPDEs for short) with reflection in a convex domain in R^k by analytical approach. The method is based on…