DeepAI
Log In Sign Up

Explicit Numerical Approximations for SDDEs in Finite and Infinite Horizons using the Adaptive EM Method: Strong Convergence and Almost Sure Exponential Stability

11/07/2022
by   Ulises Botija-Munoz, et al.
0

In this paper we investigate explicit numerical approximations for stochastic differential delay equations (SDDEs) under a local Lipschitz condition by employing the adaptive Euler-Maruyama (EM) method. Working in both finite and infinite horizons, we achieve strong convergence results by showing the boundedness of the pth moments of the adaptive EM solution. We also obtain the order of convergence infinite horizon. In addition, we show almost sure exponential stability of the adaptive approximate solution for both SDEs and SDDEs.

READ FULL TEXT

page 1

page 2

page 3

page 4

03/13/2022

Convergence of Numerical Solution of The Tamed Milstein Method for NSDDEs

In this paper, we apply the tamed technique to the Milstein numerical sc...
08/09/2021

The truncated EM method for stochastic differential delay equations with variable delay

This paper mainly investigates the strong convergence and stability of t...
09/10/2020

Convergence rate of EM algorithm for SDEs under integrability condition

In this paper, by employing Gaussian type estimate of heat kernel, we es...
12/07/2021

Explicit approximations for nonlinear switching diffusion systems in finite and infinite horizons

Focusing on hybrid diffusion dynamics involving continuous dynamics as w...