Delay tolerance for stable hybrid stochastic differential equations with Lévy noise based on Razumikhin technique

Wenrui Li; Chen Fei; Chunhui Mei; Weiyin Fei; Xuerong Mao

doi:10.1016/j.sysconle.2023.105530

Delay tolerance for stable hybrid stochastic differential equations with Lévy noise based on Razumikhin technique

Wenrui Li, Chen Fei, Chunhui Mei, Weiyin Fei, Xuerong Mao

Mathematics And Statistics

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Abstract

In this article we will study the delay tolerance for stable hybrid stochastic differential equations with Lévy noise (SDEsLN) under global Lipschitz coefficients. Based on Razumikhin technique, we will show that when the hybrid SDEs-LN without delay is pth moment exponentially stable (p-MES), the system with small delays is still p-MES. We will also obtain explicit delay bounds for p-MES. Finally, an example about neural network will be provided to illustrate the effectiveness and feasibility of theoretical results

Original language	English
Article number	105530
Journal	Systems and Control Letters
Volume	176
Early online date	21 Apr 2023
DOIs	https://doi.org/10.1016/j.sysconle.2023.105530
Publication status	Published - 1 Jun 2023

Keywords

delay tolerance
Lévy noise
pth moment exponentially stable
Razumikhin technique

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10.1016/j.sysconle.2023.105530

Li-etal-SCL-2023-Delay-tolerance-for-stable-hybrid-stochastic-differential-equationsAccepted author manuscript, 764 KBLicence: CC BY-NC-ND 4.0

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@article{7c93fa7b1970426da411ea072018e993,

title = "Delay tolerance for stable hybrid stochastic differential equations with L{\'e}vy noise based on Razumikhin technique",

abstract = "In this article we will study the delay tolerance for stable hybrid stochastic differential equations with L{\'e}vy noise (SDEsLN) under global Lipschitz coefficients. Based on Razumikhin technique, we will show that when the hybrid SDEs-LN without delay is pth moment exponentially stable (p-MES), the system with small delays is still p-MES. We will also obtain explicit delay bounds for p-MES. Finally, an example about neural network will be provided to illustrate the effectiveness and feasibility of theoretical results",

keywords = "delay tolerance, L{\'e}vy noise, pth moment exponentially stable, Razumikhin technique",

author = "Wenrui Li and Chen Fei and Chunhui Mei and Weiyin Fei and Xuerong Mao",

year = "2023",

month = jun,

day = "1",

doi = "10.1016/j.sysconle.2023.105530",

language = "English",

volume = "176",

journal = "Systems and Control Letters",

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TY - JOUR

T1 - Delay tolerance for stable hybrid stochastic differential equations with Lévy noise based on Razumikhin technique

AU - Li, Wenrui

AU - Fei, Chen

AU - Mei, Chunhui

AU - Fei, Weiyin

AU - Mao, Xuerong

PY - 2023/6/1

Y1 - 2023/6/1

N2 - In this article we will study the delay tolerance for stable hybrid stochastic differential equations with Lévy noise (SDEsLN) under global Lipschitz coefficients. Based on Razumikhin technique, we will show that when the hybrid SDEs-LN without delay is pth moment exponentially stable (p-MES), the system with small delays is still p-MES. We will also obtain explicit delay bounds for p-MES. Finally, an example about neural network will be provided to illustrate the effectiveness and feasibility of theoretical results

AB - In this article we will study the delay tolerance for stable hybrid stochastic differential equations with Lévy noise (SDEsLN) under global Lipschitz coefficients. Based on Razumikhin technique, we will show that when the hybrid SDEs-LN without delay is pth moment exponentially stable (p-MES), the system with small delays is still p-MES. We will also obtain explicit delay bounds for p-MES. Finally, an example about neural network will be provided to illustrate the effectiveness and feasibility of theoretical results

KW - delay tolerance

KW - Lévy noise

KW - pth moment exponentially stable

KW - Razumikhin technique

UR - https://www.sciencedirect.com/journal/systems-and-control-letters

U2 - 10.1016/j.sysconle.2023.105530

DO - 10.1016/j.sysconle.2023.105530

M3 - Article

SN - 0167-6911

VL - 176

JO - Systems and Control Letters

JF - Systems and Control Letters

M1 - 105530

ER -

Delay tolerance for stable hybrid stochastic differential equations with Lévy noise based on Razumikhin technique

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Long-time dynamics of numerical solutions of stochastic differential equations

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Delay tolerance for stable hybrid stochastic differential equations with Lévy noise based on Razumikhin technique

Abstract

Keywords

Access to Document

Other files and links

Fingerprint

Projects

Long-time dynamics of numerical solutions of stochastic differential equations

Cite this