Hybrid stochastic functional differential equations with infinite delay: Approximations and numerics

This paper is to investigate if the solution of a hybrid stochastic functional differential equation (SFDE) with infinite delay can be approximated by the solution of the corresponding hybrid SFDE with finite delay. A positive result is established for a large class of highly nonlinear hybrid SFDEs...

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Bibliographic Details
Published in:	Journal of Differential Equations Vol. 374; pp. 154 - 190
Main Authors:	Li, Guozhen, Li, Xiaoyue, Mao, Xuerong, Song, Guoting
Format:	Journal Article
Language:	English
Published:	Elsevier Inc 25-11-2023
Subjects:	Approximate solution Finite delay Infinite delay Numerical solution Stochastic functional differential equation Finite delay Stochastic functional differential equation Approximate solution Numerical solution Infinite delay
Online Access:	Get full text
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Summary:	This paper is to investigate if the solution of a hybrid stochastic functional differential equation (SFDE) with infinite delay can be approximated by the solution of the corresponding hybrid SFDE with finite delay. A positive result is established for a large class of highly nonlinear hybrid SFDEs with infinite delay. Our new theory makes it possible to numerically approximate the solution of the hybrid SFDE with infinite delay, via the numerical solution of the corresponding hybrid SFDE with finite delay.
ISSN:	0022-0396 1090-2732
DOI:	10.1016/j.jde.2023.07.028