Advances in the LaSalle-type theorems for stochastic functional differential equations with infinite delay

Ya Wang; Fuke Wu; Xuerong Mao; Enwen Zhu

doi:10.3934/dcdsb.2019182

Advances in the LaSalle-type theorems for stochastic functional differential equations with infinite delay

Ya Wang, Fuke Wu, Xuerong Mao, Enwen Zhu

Mathematics And Statistics

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4 Citations (Scopus)

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Abstract

This paper considers stochastic functional differential equations (SFDEs) with infinite delay. The main aim is to establish the LaSalle-type theorems to locate limit sets for this class of SFDEs. In comparison with the existing results, this paper gives more general results under the weaker conditions imposed on the Lyapunov function. These results can be used to discuss the asymptotic stability and asymptotic boundedness for SFDEs with infinite delay. In the end, two examples will be given to illustrate applications of our new results established.

Original language	English
Pages (from-to)	287-300
Number of pages	14
Journal	Discrete and Continuous Dynamical Systems - Series B
Volume	25
Issue number	1
DOIs	https://doi.org/10.3934/dcdsb.2019182
Publication status	Published - 31 Jan 2020

Keywords

stochastic functional differential equations
SFDEs
infinite delay
LaSalle-type theorems

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10.3934/dcdsb.2019182

Wang-etal-DCDS-2019-Advances-in-the-LaSalle-type-theorems-for-stochastic-functional-differential-equationsAccepted author manuscript, 356 KB

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title = "Advances in the LaSalle-type theorems for stochastic functional differential equations with infinite delay",

abstract = "This paper considers stochastic functional differential equations (SFDEs) with infinite delay. The main aim is to establish the LaSalle-type theorems to locate limit sets for this class of SFDEs. In comparison with the existing results, this paper gives more general results under the weaker conditions imposed on the Lyapunov function. These results can be used to discuss the asymptotic stability and asymptotic boundedness for SFDEs with infinite delay. In the end, two examples will be given to illustrate applications of our new results established.",

keywords = "stochastic functional differential equations, SFDEs, infinite delay, LaSalle-type theorems",

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T1 - Advances in the LaSalle-type theorems for stochastic functional differential equations with infinite delay

AU - Wang, Ya

AU - Wu, Fuke

AU - Mao, Xuerong

AU - Zhu, Enwen

PY - 2020/1/31

Y1 - 2020/1/31

N2 - This paper considers stochastic functional differential equations (SFDEs) with infinite delay. The main aim is to establish the LaSalle-type theorems to locate limit sets for this class of SFDEs. In comparison with the existing results, this paper gives more general results under the weaker conditions imposed on the Lyapunov function. These results can be used to discuss the asymptotic stability and asymptotic boundedness for SFDEs with infinite delay. In the end, two examples will be given to illustrate applications of our new results established.

AB - This paper considers stochastic functional differential equations (SFDEs) with infinite delay. The main aim is to establish the LaSalle-type theorems to locate limit sets for this class of SFDEs. In comparison with the existing results, this paper gives more general results under the weaker conditions imposed on the Lyapunov function. These results can be used to discuss the asymptotic stability and asymptotic boundedness for SFDEs with infinite delay. In the end, two examples will be given to illustrate applications of our new results established.

KW - stochastic functional differential equations

KW - SFDEs

KW - infinite delay

KW - LaSalle-type theorems

UR - http://www.aimsciences.org/journal/1531-3492

U2 - 10.3934/dcdsb.2019182

DO - 10.3934/dcdsb.2019182

M3 - Article

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VL - 25

SP - 287

EP - 300

JO - Discrete and Continuous Dynamical Systems - Series B

JF - Discrete and Continuous Dynamical Systems - Series B

IS - 1

ER -

Advances in the LaSalle-type theorems for stochastic functional differential equations with infinite delay

Abstract

Keywords

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Ergodicity and invariant measures of stochastic delay systems driven by various noises and their applications (Prof. Fuke Wu)

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Advances in the LaSalle-type theorems for stochastic functional differential equations with infinite delay

Abstract

Keywords

Access to Document

Other files and links

Fingerprint

Projects

Ergodicity and invariant measures of stochastic delay systems driven by various noises and their applications (Prof. Fuke Wu)

Cite this