Related papers: Strong Predictor-Corrector Euler-Maruyama Methods …
The backward Euler-Maruyama (BEM) method is employed to approximate the invariant measure of stochastic differential equations, where both the drift and the diffusion coefficient are allowed to grow super-linearly. The existence and…
This article investigates the Euler-Maruyama approximation procedure for stochastic differential equations in the framework of G-Browinian motion with non-linear growth and non-Lipschitz conditions. Subject to non-linear growth condition,…
We address the weak numerical solution of stochastic differential equations driven by independent Brownian motions (SDEs for short). This paper develops a new methodology to design adaptive strategies for determining automatically the…
The aim of this paper is to study weak and strong convergence of the Euler--Maruyama scheme for a solution of one-dimensional degenerate stochastic differential equation $\mathrm{d} X_t=\sigma(X_t) \mathrm{d} W_t$ with non-sticky condition.…
Stochastic differential equations (sdes) play an important role in physics but existing numerical methods for solving such equations are of low accuracy and poor stability. A general strategy for developing accurate and efficient schemes…
The existence and uniqueness of the numerical invariant measure of the backward Euler-Maruyama method for stochastic differential equations with Markovian switching is yielded, and it is revealed that the numerical invariant measure…
We introduce a new approach for designing numerical schemes for stochastic differential equations (SDEs). The approach, which we have called direction and norm decomposition method, proposes to approximate the required solution $X_t$ by…
This work establishes the weak convergence of Euler-Maruyama's approximation for stochastic differential equations (SDEs) with singular drifts under the integrability condition in lieu of the widely used growth condition. This method is…
The stochastic heat equation on the sphere driven by additive isotropic Wiener noise is approximated by a spectral method in space and forward and backward Euler-Maruyama schemes in time. The spectral approximation is based on a truncation…
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 presents and analyzes the compensated projected Euler-Maruyama method for stochastic differential equations with jumps under a global monotonicity condition. Compared with existing conditions, this condition allows the…
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…
In this paper, we investigate the problem of strong approximation of the solutions of stochastic differential equations (SDEs) when the drift coefficient is given in integral form. We investigate its upper error bounds, in terms of the…
This paper aims at developing a systematic study for the weak rate of convergence of the Euler-Maruyama scheme for stochastic differential equations with very irregular drift and constant diffusion coefficients. We apply our method to…
This paper introduces time-continuous numerical schemes to simulate stochastic differential equations (SDEs) arising in mathematical finance, population dynamics, chemical kinetics, epidemiology, biophysics, and polymeric fluids. These…
Building on the well-posedness of the backward Kolmogorov partial differential equation in the Wasserstein space, we analyze the strong and weak convergence rates for approximating the unique solution of a class of McKean-Vlasov stochastic…
Exponential integrability properties of numerical approximations are a key tool for establishing positive rates of strong and numerically weak convergence for a large class of nonlinear stochastic differential equations. It turns out that…
The efficient management of large-scale queueing networks is critical for a variety of sectors, including healthcare, logistics, and customer service, where system performance has profound implications for operational effectiveness and cost…
This paper is concerned with the numerical approximation of stochastic ordinary differential equations, which satisfy a global monotonicity condition. This condition includes several equations with super-linearly growing drift and diffusion…
We study the strong $L^p$-convergence rates of the Euler-Maruyama method for stochastic differential equations driven by Brownian motion with low-regularity drift coefficients. Specifically, the drift is assumed to be in the…