相关论文: Trotter-Kato approximations of semilinear stochast…

This paper studies a class of impulsive neutral stochastic partial differential equations in real Hilbert spaces. The main goal here is to consider the Trotter-Kato approximations of mild solutions of such equations in the $p$th-mean…

This paper is devoted to studying abstract stochastic semilinear evolution equations with additive noise in Hilbert spaces. First, we prove the existence of unique local mild solutions and show their regularity. Second, we show the regular…

We prove that the mild solution to a semilinear stochastic evolution equation on a Hilbert space, driven by either a square integrable martingale or a Poisson random measure, is (jointly) continuous, in a suitable topology, with respect to…

This paper addresses the existence of nonnegative mild solutions for stochastic evolution inclusions through a weak topology approach. Precisely, the study focuses on stochastic evolution inclusions characterized by multivalued…

The paper is devoted to evolution equations of the form $\partial$ $\partial$t u(t) = --(A + B(t))u(t), t $\in$ I = [0, T ], on separable Hilbert spaces where A is a non-negative self-adjoint operator and B($\times$) is family of…

In this paper we study the numerical method for approximating the random periodic solution of semiliear stochastic evolution equations. The main challenge lies in proving a convergence over an infinite time horizon while simulating…

Semilinear stochastic evolution equations with L\'evy noise and monotone nonlinear drift are considered. The existence and uniqueness of the mild solutions in $L^p$ for these equations is proved and a sufficient condition for exponential…

We treat the convergence of Carleman linearization of nonlinear evolutionary equations through the approximation theory of strongly continuous semigroups, by Carleman embedding the underlying nonlinear semigroups as linear semigroups.…

In the semigroup approach to stochastic evolution equations, the fundamental issue of uniqueness of mild solutions is often "reduced" to the much easier problem of proving uniqueness for strong solutions. This reduction is usually carried…

In this article we propose a new, explicit and easily implementable numerical method for approximating a class of semilinear stochastic evolution equations with non-globally Lipschitz continuous nonlinearities. We establish strong…

The mild Ito formula proposed in Theorem 1 in [Da Prato, G., Jentzen, A., \& R\"ockner, M., A mild Ito formula for SPDEs, arXiv:1009.3526 (2012), To appear in the Trans.\ Amer.\ Math.\ Soc.] has turned out to be a useful instrument to study…

In this paper we develop a new approach to stochastic evolution equations with an unbounded drift $A$ which is dependent on time and the underlying probability space in an adapted way. It is well-known that the semigroup approach to…

We investigate the quality of space approximation of a class of stochastic integral equations of convolution type with Gaussian noise. Such equations arise, for example, when considering mild solutions of stochastic fractional order partial…

Semilinear stochastic evolution equations with multiplicative L\'evy noise and monotone nonlinear drift are considered. Unlike other similar work we do not impose coercivity conditions on coefficients. Existence and uniqueness of the mild…

We prove a limit theorem for quantum stochastic differential equations with unbounded coefficients which extends the Trotter-Kato theorem for contraction semigroups. From this theorem, general results on the convergence of approximations…

We consider the Cauchy problem for a semilinear stochastic differential inclusion in a Hilbert space. The linear operator generates a strongly continuous semigroup and the nonlinear term is multivalued and satisfies a condition which is…

Existence and uniqueness for semilinear stochastic evolution equations with additive noise by means of finite dimensional Galerkin approximations is established and the convergence rate of the Galerkin approximations to the solution of the…

Semilinear stochastic evolution equations with multiplicative Poisson noise and monotone nonlinear drift are considered. We do not impose coercivity conditions on coefficients. A novel method of proof for establishing existence and…

Structured population models are a class of general evolution equations which are widely used in the study of biological systems. Many theoretical methods are available for establishing existence and stability of steady states of general…

Existence and uniqueness of mild solutions to a class of semilinear stochastic evolution equations with additive noise is proved. The linear part of the drift term is the generator of a compact semigroup of contractions, while the nonlinear…