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

Guozhen Li; Xiaoyue  Li; Xuerong Mao; Guoting Song

doi:10.1016/j.jde.2023.07.028

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

Guozhen Li, Xiaoyue Li, Xuerong Mao, Guoting Song

Mathematics And Statistics

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Abstract

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.

Original language	English
Pages (from-to)	154-190
Number of pages	37
Journal	Journal of Differential Equations
Volume	374
Early online date	4 Aug 2023
DOIs	https://doi.org/10.1016/j.jde.2023.07.028
Publication status	Published - 25 Nov 2023

Keywords

stochastic functional differential equations
infinite delay
finite delay
approximate solution
numerical solution

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10.1016/j.jde.2023.07.028Licence: CC BY 4.0

Li-etal-JDE-2023-Hybrid-stochastic-functional-differential-equations-with-infinite-delayFinal published version, 676 KBLicence: CC BY 4.0

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title = "Hybrid stochastic functional differential equations with infinite delay: approximations and numerics",

abstract = "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.",

keywords = "stochastic functional differential equations, infinite delay, finite delay, approximate solution, numerical solution",

author = "Guozhen Li and Xiaoyue Li and Xuerong Mao and Guoting Song",

year = "2023",

month = nov,

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doi = "10.1016/j.jde.2023.07.028",

language = "English",

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journal = "Journal of Differential Equations",

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TY - JOUR

T1 - Hybrid stochastic functional differential equations with infinite delay

T2 - approximations and numerics

AU - Li, Guozhen

AU - Li, Xiaoyue

AU - Mao, Xuerong

AU - Song, Guoting

PY - 2023/11/25

Y1 - 2023/11/25

N2 - 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.

AB - 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.

KW - stochastic functional differential equations

KW - infinite delay

KW - finite delay

KW - approximate solution

KW - numerical solution

UR - https://www.sciencedirect.com/journal/journal-of-differential-equations

U2 - 10.1016/j.jde.2023.07.028

DO - 10.1016/j.jde.2023.07.028

M3 - Article

SN - 0022-0396

VL - 374

SP - 154

EP - 190

JO - Journal of Differential Equations

JF - Journal of Differential Equations

ER -

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

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Long-time dynamics of numerical solutions of stochastic differential equations

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

Abstract

Keywords

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Long-time dynamics of numerical solutions of stochastic differential equations

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