DeepAI
Log In Sign Up

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

08/09/2021
by   Shounian Deng, et al.
0

This paper mainly investigates the strong convergence and stability of the truncated Euler-Maruyama (EM) method for stochastic differential delay equations with variable delay whose coefficients can be growing super-linearly. By constructing appropriate truncated functions to control the super-linear growth of the original coefficients, we present a type of the truncated EM method for such SDDEs with variable delay, which is proposed to be approximated by the value taken at the nearest grid points on the left of the delayed argument. The strong convergence result (without order) of the method is established under the local Lipschitz plus generalized Khasminskii-type conditions and the optimal strong convergence order 1/2 can be obtained if the global monotonicity with U function and polynomial growth conditions are added to the assumptions. Moreover, the partially truncated EM method is proved to preserve the mean-square and H_∞stabilities of the true solutions. Compared with the known results on the truncated EM method for SDDEs, a better order of strong convergence is obtained under more relaxing conditions on the coefficients, and more refined technical estimates are developed so as to overcome the challenges arising due to variable delay. Lastly, some numerical examples are utilized to confirm the effectiveness of the theoretical results.

READ FULL TEXT

page 1

page 2

page 3

page 4

10/11/2022

Evaluation of Delay Uncertainty in PCB Interconnects Due to Fiber Weave Effect

Delay Deviation Exceedance (DDE) and Differential Skew Exceedance (DSE) ...
07/28/2019

Equivalence of pth moment stability between stochastic differential delay equations and their numerical methods

In this paper, a general theorem on the equivalence of pth moment stabil...
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...