Related papers: Discretization error of Stochastic Integrals

This paper is concerned with the adaptive numerical treatment of stochastic partial differential equations. Our method of choice is Rothe's method. We use the implicit Euler scheme for the time discretization. Consequently, in each step, an…

In traditional work on numerical schemes for solving stochastic differential equations (SDEs), it is usually assumed that the coefficients are globally Lipschitz. This assumption has been used to establish a powerful analysis of the…

Stochastic differential equations with noisy memory are often impossible to solve analytically. Therefore, we derive a numerical Euler-Maruyama scheme for such equations and prove that the mean-square error of this scheme is of order…

In this paper we consider the Euler-Maruyama scheme for a class ofstochastic delay differential equations driven by a fractional Brownian motion with index $H\in(0,1)$. We establish the consistency of the scheme and study the rate of…

The purpose of this paper is to establish the convergence in distribution of the normalized error in the Euler approximation scheme for stochastic Volterra equations driven by a standard Brownian motion, with a kernel of the form…

For an unknown continuous distribution on a real line, we consider the approximate estimation by the discretization. There are two methods for the discretization. First method is to divide the real line into several intervals before taking…

Practical diffusion sampling is a numerical approximation problem: under a fixed inference budget, one must simulate a reverse-time ODE or SDE using only a limited number of denoising steps, so discretization error is often the dominant…

We study geometric stochastic differential equations (SDEs) and their approximations on Riemannian manifolds. In particular, we introduce a simple new construction of geometric SDEs, using which with bounded curvature. In particular, we…

We study the strong approximation of stochastic differential equations with discontinuous drift coefficients and (possibly) degenerate diffusion coefficients. To account for the discontinuity of the drift coefficient we construct an…

General stochastic Euler schemes for ordinary differential equations are studied. We give proofs on the consistency, the rate of convergence and the asymptotic normality of these procedures.

The (asymptotic) behaviour of the second moment of solutions to stochastic differential equations is treated in mean-square stability analysis. This property is discussed for approximations of infinite-dimensional stochastic differential…

The paper considers an Euler discretization based numerical scheme for approximating functionals of invariant distribution of an ergodic diffusion. Convergence of the numerical scheme is shown for suitably chosen discretization step, and a…

This paper aims to investigate the asymptotic error distribution of several numerical methods for stochastic partial differential equations (SPDEs) with multiplicative noise. Firstly, we give the limit distribution of the normalized error…

We consider a pointwise tracking optimal control problem for a semilinear elliptic partial differential equation. We derive the existence of optimal solutions and analyze first and, necessary and sufficient, second order optimality…

In this paper, we investigate the asymptotic distribution of the normalized error for the Mittag--Leffler Euler (MLE) method applied to a class of multidimensional fractional stochastic differential equations. These equations are…

We study the approximation of certain stochastic integrals with respect to a d-dimensional diffusion by corresponding stochastic integrals with piece-wise constant integrands. In finance this corresponds to replacing a continuously adjusted…

This paper aims to investigate the distributed stochastic optimization problems on compact embedded submanifolds (in the Euclidean space) for multi-agent network systems. To address the manifold structure, we propose a distributed…

The asymptotic error distribution of numerical methods applied to stochastic ordinary differential equations has been well studied, which characterizes the evolution pattern of the error distribution in the small step-size regime. It is…

The maximum entropy principle is a powerful tool for solving underdetermined inverse problems. This paper considers the problem of discretizing a continuous distribution, which arises in various applied fields. We obtain the approximating…

A fully discrete approximation of the semi-linear stochastic wave equation driven by multiplicative noise is presented. A standard linear finite element approximation is used in space and a stochastic trigonometric method for the temporal…