DeepAI
Log In Sign Up

Mean-square convergence and stability of the backward Euler method for stochastic differential delay equations with highly nonlinear growing coefficients

09/20/2022
by   Zhuoqi Liu, et al.
0

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 technique, this paper focuses on the mean-square convergence and stability of the backward Euler method (BEM) for SDDEs whose drift and diffusion coefficients can both grow polynomially. The upper mean-square error bounds of BEM are obtained. Then the convergence rate, which is one-half, is revealed without using the moment boundedness of numerical solutions. Furthermore, under fairly general conditions, the novel technique is applied to prove that the BEM can inherit the exponential mean-square stability with a simple proof. At last, two numerical experiments are implemented to illustrate the reliability of the theories.

READ FULL TEXT

page 1

page 2

page 3

page 4

02/21/2020

On the backward Euler method for a generalized Ait-Sahalia-type rate model with Poisson jumps

This article aims to reveal the mean-square convergence rate of the back...
09/10/2020

Mean-square contractivity of stochastic θ-methods

The paper is focused on the nonlinear stability analysis of stochastic θ...
06/27/2019

Error estimates of the backward Euler-Maruyama method for multi-valued stochastic differential equations

In this paper, we derive error estimates of the backward Euler-Maruyama ...
12/21/2021

The truncated θ-Milstein method for nonautonomous and highly nonlinear stochastic differential delay equations

This paper focuses on the strong convergence of the truncated θ-Milstein...
11/10/2022

Error bound analysis of the stochastic parareal algorithm

Stochastic parareal (SParareal) is a probabilistic variant of the popula...