Related papers: Non-asymptotic Error Analysis of Explicit Modified…
This article introduces and analyzes a new explicit, easily implementable, and full discrete accelerated exponential Euler-type approximation scheme for additive space-time white noise driven stochastic partial differential equations…
Minimum expected distance estimation (MEDE) algorithms have been widely used for probabilistic models with intractable likelihood functions and they have become increasingly popular due to their use in implicit generative modeling (e.g.…
In this paper, we study the numerical simulations for Euler system with maximal density constraint. This model is developed in [1, 3] with the constraint introduced into the system by a singular pressure law, which causes the transition of…
This paper aims to investigate the numerical approximation of a general second order parabolic stochastic partial differential equation(SPDE) driven by multiplicative and additive noise under more relaxed conditions. The SPDE is discretized…
We obtain non asymptotic bounds for the Monte Carlo algorithm associated to the Euler discretization of some diffusion processes. The key tool is the Gaussian concentration satisfied by the density of the discretization scheme. This…
In this paper, we are concerned with a modified Euler scheme for the SDE under consideration, where the drift is of super-linear growth and dissipative merely outside a closed ball. By adopting the synchronous coupling, along with the…
This paper establishes the first-order convergence rate for the ergodic error of numerical approximations to a class of stochastic ODEs (SODEs) with superlinear coefficients and multiplicative noise. By leveraging the generator approach to…
The present paper introduces a class of finite volume schemes of increasing order of accuracy in space and time for hyperbolic systems that are in conservation form. This paper specifically focuses on Euler system that is used for modeling…
The design and analysis of a unified asymptotic preserving (AP) and well-balanced scheme for the Euler Equations with gravitational and frictional source terms is presented in this paper. The asymptotic behaviour of the Euler system in the…
We prove a general criterion providing sufficient conditions under which a time-discretiziation of a given Stochastic Differential Equation (SDE) is a uniform in time approximation of the SDE. The criterion is also, to a certain extent,…
We consider numerical approximations of stochastic differential equations by the Euler method. In the case where the SDE is elliptic or hypoelliptic, we show a weak backward error analysis result in the sense that the generator associated…
Although generative diffusion models (GDMs) are widely used in practice, their theoretical foundations remain limited, especially concerning the impact of different discretization schemes applied to the underlying stochastic differential…
Our subject of study is strong approximation of stochastic differential equations (SDEs) with respect to the supremum error criterion, and we seek approximations that are strongly asymptotically optimal in specific classes of…
We discrete the ergodic semilinear stochastic partial differential equations in space dimension $d \leq 3$ with additive noise, spatially by a spectral Galerkin method and temporally by an exponential Euler scheme. It is shown that both the…
Stochastic approximation (SA) is a method for finding the root of an operator perturbed by noise. There is a rich literature establishing the asymptotic normality of rescaled SA iterates under fairly mild conditions. However, these…
We consider a parameter dependent family of damped hyperbolic equations with interesting limit behavior: the system approaches steady states exponentially fast and for parameter to zero the solutions converge to that of a parabolic limit…
For stochastic differential equations (SDEs) with Markovian switching, whose drift and diffusion coefficients are allowed to contain superlinear terms, the backward Euler-Maruyama (BEM) method is proposed to approximate the invariant…
Over the last few decades, the numerical methods for stochastic differential delay equations (SDDEs) have been investigated and developed by many scholars. Nevertheless, there is still little work to be completed. By virtue of the novel…
In this paper, we are interested in deriving non-asymptotic error bounds for the multilevel Monte Carlo method. As a first step, we deal with the explicit Euler discretization of stochastic differential equations with a constant diffusion…
In this article we introduce several kinds of easily implementable explicit schemes, which are amenable to Khasminski's techniques and are particularly suitable for highly nonlinear stochastic differential equations (SDEs). We show that…