相关论文: Strong Convergence Rates for Euler Schemes of Levy…

In this paper we extend existing results on the numerical approximation of one-dimensional SDEs with drift in a negative order Besov space and driven by Brownian motion. Using the Yamada-Watanabe approximation technique, we prove rates in…

We develop and analyze a general class of Euler-type numerical schemes for Levy-driven McKean-Vlasov stochastic differential equations (SDEs), where the drift, diffusion and jump coefficients grow super-linearly in the state variable. These…

We investigate some recursive procedures based on an exact or ``approximate'' Euler scheme with decreasing step in vue to computation of invariant measures of solutions to S.D.E. driven by a L\'evy process. Our results are valid for a large…

Euler-Maruyama method is studied to approximate stochastic differential equations driven by the symmetric $\alpha$-stable additive noise with the $\beta$ H\"older continuous drift coefficient. When $\alpha \in (1,2)$ and $\beta \in…

This paper focuses on the strong convergence rate of both Runge--Kutta methods and simplified step-$N$ Euler schemes for stochastic differential equations driven by multi-dimensional fractional Brownian motions with $H\in(\frac12,1)$. Based…

In this paper numerical methods for solving stochastic differential equations with Markovian switching (SDEwMSs) are developed by pathwise approximation. The proposed family of strong predictor-corrector Euler-Maruyama methods is designed…

Motivated by truncated EM method introduced by Mao (2015), a new explicit numerical method named modified truncated Euler-Maruyama method is developed in this paper. Strong convergence rates of the given numerical scheme to the exact…

In this paper, we study a class of super-linear stochastic differential delay equations with Poisson jumps (SDDEwPJs). The convergence and rate of the convergence of the truncated Euler-Maruyama numerical solutions to SDDEwPJs are…

We study the temporal-spatial regularity properties of tamed Euler approximations for L\'evy-driven SDEs with superlinearly growing drift and diffusion coefficients. We first introduce a novel tamed Euler-type scheme and establish its…

We study strong approximation of $d$-dimensional stochastic differential equations (SDEs) with a discontinuous drift coefficient. More precisely, we essentially assume that the drift coefficient is piecewise Lipschitz continuous with an…

Most existing literature focuses on pointwise convergence (i.e., convergence at a fixed time point) of numerical solutions for Stochastic functional differential equations (SFDEs). In contrast, this paper investigates the strong segment…

In this paper, we consider scalar stochastic differential equations (SDEs) with a superlinearly growing and piecewise continuous drift coefficient. Existence and uniqueness of strong solutions of such SDEs are obtained. Furthermore, the…

In this paper we study strong approximation of the solution of a scalar stochastic differential equation (SDE) at the final time in the case when the drift coefficient may have discontinuities in space. Recently it has been shown in…

The Euler scheme is one of the standard schemes to obtain numerical approximations of stochastic differential equations (SDEs). Its convergence properties are well-known in the case of globally Lipschitz continuous coefficients. However, in…

In this article, we are interested in the strong well-posedness together with the numerical approximation of some one-dimensional stochastic differential equations with a non-linear drift, in the sense of McKean-Vlasov, driven by a…

We prove strong convergence of order $1/4-\epsilon$ for arbitrarily small $\epsilon>0$ of the Euler-Maruyama method for multidimensional stochastic differential equations (SDEs) with discontinuous drift and degenerate diffusion coefficient.…

The paper estimates the rate of convergence of the weak Euler approximation for the solutions of SDEs with Hoelder continuous coefficients driven by point and martingale measures. The equation considered has a non-degenerate main part whose…

In this paper, we establish the weak convergence rate of density-dependent stochastic differential equations with bounded drift driven by $\alpha$-stable processes with $\alpha\in(1,2)$. The well-posedness of these equations has been…

In this paper, we are concerned with convergence rate of Euler-Maruyama scheme for stochastic differential equations with rough coefficients. The key contributions lie in (i), by means of regularity of non-degenerate Kolmogrov equation, we…

We propose new jump-adapted weak approximation schemes for stochastic differential equations driven by pure-jump L\'evy processes. The idea is to replace the driving L\'evy process $Z$ with a finite intensity process which has the same…