相关论文: Approximating the coefficients in semilinear stoch…

We study mild solutions of a class of stochastic partial differential equations, involving operators with polynomially bounded coefficients. We consider semilinear equations under suitable hyperbolicity hypotheses on the linear part. We…

In this paper, we establish the well-posedness and optimal trajectory regularity for the solution of stochastic evolution equations with generalized Lipschitz-type coefficients driven by general multiplicative noises. To ensure the…

We consider the long-time behavior of an explicit tamed exponential Euler scheme applied to a class of parabolic semilinear stochastic partial differential equations driven by additive noise, under a one-sided Lipschitz continuity…

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 present a way of treating stochastic partial differential equations with multiplicative noise by rewriting them as stochastically perturbed evolutionary equations in the sense of \cite{picardbook}, where a general…

Let $A,C,P:D(A)\subset X\to X$ be linear operators on a Banach space $X$ such that $-A$ generates a strongly continuous semigroup on $X$, and $F:X\to X$ be a globally Lipschitz function. We study the well-posedness of semilinear equations…

We introduce the local martingale problem associated to semilinear stochastic evolution equations driven by a cylindrical Wiener process and establish a one-to-one correspondence between solutions of the martingale problem and…

Semilinear, $N-$dimensional stochastic differential equations (SDEs) driven by additive L\'evy noise are investigated. Specifically, given $\alpha\in\left(\frac{1}{2},1\right)$, the interest is on SDEs driven by $2\alpha-$stable,…

We consider a class of semilinear Volterra type stochastic evolution equation driven by multiplicative Gaussian noise. The memory kernel, not necessarily analytic, is such that the deterministic linear equation exhibits a parabolic…

We obtain necessary and sufficient conditions for equivalence of law for linear stochastic evolution equations driven by a general Gaussian noise by identifying the suitable space of controls for the corresponding deterministic control…

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…

Known investigations of nonlinear evolution equations $${dx\over dt} + A(t)x(t) = f(t)\ ,\quad x(t_{0}) = x^{0},\ \quad t_{0} \le t < \infty\ , \eqno(0.1)$$ with monotone operators $A(t)$ acting from reflexive Banach space $B$ to dual space…

We introduce a stochastic partial differential equation (SPDE) with elliptic operator in divergence form, with measurable and bounded coefficients and driven by space-time white noise. Such SPDEs could be used in mathematical modelling of…

In this paper, we investigate a semilinear stochastic parabolic equation with a linear rough term $du_{t}=\left[L_{t}u_{t}+f\left(t, u_{t}\right)\right]dt+\left(G_{t}u_{t}+g_{t}\right)d\mathbf{X}_{t}+h\left(t, u_{t}\right)dW_{t}$, where…

Efficient simulation of stochastic partial differential equations (SPDE) on general domains requires noise discretization. This paper employs piecewise linear interpolation of noise in a fully discrete finite element approximation of a…

In this paper, we consider the numerical approximation of a general second order semilinear stochastic partial differential equation (SPDE) driven by multiplicative and additive noise. Our main interest is on such SPDEs where the nonlinear…

Stochastic partial differential equations (SPDEs) are the mathematical tool of choice for modelling spatiotemporal PDE-dynamics under the influence of randomness. Based on the notion of mild solution of an SPDE, we introduce a novel neural…

In this article we prove pathwise Holder convergence with optimal rates of the implicit Euler scheme for semi-linear parabolic stochastic differential equations with multiplicative noise, set in a UMD Banach space X. We assume the…

We prove existence, uniqueness and Lipschitz dependence on the initial datum for mild solutions of stochastic partial differential equations with Lipschitz coefficients driven by Wiener and Poisson noise. Under additional assumptions, we…

This paper considers a general framework for the study of the existence of quasi-variational and variational solutions to a class of nonlinear evolution systems in convex sets of Banach spaces describing constraints on a linear combination…