Stability of highly nonlinear hybrid stochastic integro-differential delay equations

Chen Fei, Mingxuan Shen, Weiyin Fei, Xuerong Mao, Litan Yan

Research output: Contribution to journalArticle

4 Citations (Scopus)

Abstract

For the past few decades, the stability criteria for the stochastic differential delay equations (SDDEs) have been studied intensively. Most of these criteria can only be applied to delay equations where their coefficients are either linear or nonlinear but bounded by linear functions. Recently, the stability criterion for highly nonlinear hybrid stochastic differential equations is investigated in Fei et al. (2017). In this paper, we investigate a class of highly nonlinear hybrid stochastic integro-differential delay equations (SIDDEs). First, we establish the stability and boundedness of hybrid stochastic integro-differential delay equations. Then the delay-dependent criteria of the stability and boundedness of solutions to SIDDEs are studied. Finally, an illustrative example is provided.
LanguageEnglish
Pages180-199
Number of pages20
JournalNonlinear Analysis: Hybrid Systems
Volume31
Early online date1 Oct 2018
DOIs
Publication statusPublished - 28 Feb 2019

Fingerprint

Differential Delay Equations
Stability criteria
Integro-differential Equation
Stability Criteria
Stochastic Differential Delay Equations
Delay-dependent Criteria
Boundedness of Solutions
Differential equations
Delay Equations
Stability of Solutions
Linear Function
Stochastic Equations
Boundedness
Differential equation
Coefficient

Keywords

  • stochastic integro-differential delay equation (SIDDE)
  • nonlinear growth condition
  • asymptotic stability
  • Markovian switching
  • Lyapunov functional

Cite this

Fei, Chen ; Shen, Mingxuan ; Fei, Weiyin ; Mao, Xuerong ; Yan, Litan. / Stability of highly nonlinear hybrid stochastic integro-differential delay equations. In: Nonlinear Analysis: Hybrid Systems. 2019 ; Vol. 31. pp. 180-199.
@article{c4c195f5cdc04c489e3c1fc9844f49e6,
title = "Stability of highly nonlinear hybrid stochastic integro-differential delay equations",
abstract = "For the past few decades, the stability criteria for the stochastic differential delay equations (SDDEs) have been studied intensively. Most of these criteria can only be applied to delay equations where their coefficients are either linear or nonlinear but bounded by linear functions. Recently, the stability criterion for highly nonlinear hybrid stochastic differential equations is investigated in Fei et al. (2017). In this paper, we investigate a class of highly nonlinear hybrid stochastic integro-differential delay equations (SIDDEs). First, we establish the stability and boundedness of hybrid stochastic integro-differential delay equations. Then the delay-dependent criteria of the stability and boundedness of solutions to SIDDEs are studied. Finally, an illustrative example is provided.",
keywords = "stochastic integro-differential delay equation (SIDDE), nonlinear growth condition, asymptotic stability, Markovian switching, Lyapunov functional",
author = "Chen Fei and Mingxuan Shen and Weiyin Fei and Xuerong Mao and Litan Yan",
year = "2019",
month = "2",
day = "28",
doi = "10.1016/j.nahs.2018.09.001",
language = "English",
volume = "31",
pages = "180--199",
journal = "Nonlinear Analysis: Hybrid Systems",
issn = "1751-570X",

}

Stability of highly nonlinear hybrid stochastic integro-differential delay equations. / Fei, Chen; Shen, Mingxuan; Fei, Weiyin; Mao, Xuerong; Yan, Litan.

In: Nonlinear Analysis: Hybrid Systems, Vol. 31, 28.02.2019, p. 180-199.

Research output: Contribution to journalArticle

TY - JOUR

T1 - Stability of highly nonlinear hybrid stochastic integro-differential delay equations

AU - Fei, Chen

AU - Shen, Mingxuan

AU - Fei, Weiyin

AU - Mao, Xuerong

AU - Yan, Litan

PY - 2019/2/28

Y1 - 2019/2/28

N2 - For the past few decades, the stability criteria for the stochastic differential delay equations (SDDEs) have been studied intensively. Most of these criteria can only be applied to delay equations where their coefficients are either linear or nonlinear but bounded by linear functions. Recently, the stability criterion for highly nonlinear hybrid stochastic differential equations is investigated in Fei et al. (2017). In this paper, we investigate a class of highly nonlinear hybrid stochastic integro-differential delay equations (SIDDEs). First, we establish the stability and boundedness of hybrid stochastic integro-differential delay equations. Then the delay-dependent criteria of the stability and boundedness of solutions to SIDDEs are studied. Finally, an illustrative example is provided.

AB - For the past few decades, the stability criteria for the stochastic differential delay equations (SDDEs) have been studied intensively. Most of these criteria can only be applied to delay equations where their coefficients are either linear or nonlinear but bounded by linear functions. Recently, the stability criterion for highly nonlinear hybrid stochastic differential equations is investigated in Fei et al. (2017). In this paper, we investigate a class of highly nonlinear hybrid stochastic integro-differential delay equations (SIDDEs). First, we establish the stability and boundedness of hybrid stochastic integro-differential delay equations. Then the delay-dependent criteria of the stability and boundedness of solutions to SIDDEs are studied. Finally, an illustrative example is provided.

KW - stochastic integro-differential delay equation (SIDDE)

KW - nonlinear growth condition

KW - asymptotic stability

KW - Markovian switching

KW - Lyapunov functional

UR - https://www.journals.elsevier.com/nonlinear-analysis-hybrid-systems

U2 - 10.1016/j.nahs.2018.09.001

DO - 10.1016/j.nahs.2018.09.001

M3 - Article

VL - 31

SP - 180

EP - 199

JO - Nonlinear Analysis: Hybrid Systems

T2 - Nonlinear Analysis: Hybrid Systems

JF - Nonlinear Analysis: Hybrid Systems

SN - 1751-570X

ER -