Stability in distribution of stochastic functional differential equations

Ya Wang; Fuke Wu; Xuerong Mao

doi:10.1016/j.sysconle.2019.104513

Stability in distribution of stochastic functional differential equations

Ya Wang, Fuke Wu, Xuerong Mao

Mathematics And Statistics

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Abstract

In this paper we investigate the stability in distribution for a class of stochastic functional differential equations (SFDEs), which include stochastic differential delay equations (SDDEs). Although stability in distribution has been studied by several authors recently, there is so far no stability-in-distribution criterion on SFDEs where the terms involved the delay components are highly nonlinear (not bounded by linear functions). In this paper we will establish the sufficient criteria on the stability in distribution for a class of highly nonlinear SFDEs. Two examples will be given to illustrate our new results. We also explain the reason why the existing stability-in-distribution criteria are not applicable by these two examples.

Original language	English
Article number	104513
Pages (from-to)	1-10
Number of pages	10
Journal	Systems and Control Letters
Volume	132
Early online date	20 Aug 2019
DOIs	https://doi.org/10.1016/j.sysconle.2019.104513
Publication status	Published - 1 Oct 2019

Keywords

stochastic functional differential equations
stability in distribution
Ito formula
Brownian motion

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10.1016/j.sysconle.2019.104513

Wang-etal-SCL-2019-Stability-in-distribution-of-stochastic-functional-differentialAccepted author manuscript, 312 KB

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title = "Stability in distribution of stochastic functional differential equations",

abstract = "In this paper we investigate the stability in distribution for a class of stochastic functional differential equations (SFDEs), which include stochastic differential delay equations (SDDEs). Although stability in distribution has been studied by several authors recently, there is so far no stability-in-distribution criterion on SFDEs where the terms involved the delay components are highly nonlinear (not bounded by linear functions). In this paper we will establish the sufficient criteria on the stability in distribution for a class of highly nonlinear SFDEs. Two examples will be given to illustrate our new results. We also explain the reason why the existing stability-in-distribution criteria are not applicable by these two examples.",

keywords = "stochastic functional differential equations, stability in distribution, Ito formula, Brownian motion",

author = "Ya Wang and Fuke Wu and Xuerong Mao",

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T1 - Stability in distribution of stochastic functional differential equations

AU - Wang, Ya

AU - Wu, Fuke

AU - Mao, Xuerong

N1 - © 2019 Elsevier B.V. All rights reserved. Ya Wang, Fuke Wu, Xuerong Mao, Stability in distribution of stochastic functional differential equations, Systems & Control Letters, Volume 132, 2019, 104513, https://doi.org/10.1016/j.sysconle.2019.104513

PY - 2019/10/1

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N2 - In this paper we investigate the stability in distribution for a class of stochastic functional differential equations (SFDEs), which include stochastic differential delay equations (SDDEs). Although stability in distribution has been studied by several authors recently, there is so far no stability-in-distribution criterion on SFDEs where the terms involved the delay components are highly nonlinear (not bounded by linear functions). In this paper we will establish the sufficient criteria on the stability in distribution for a class of highly nonlinear SFDEs. Two examples will be given to illustrate our new results. We also explain the reason why the existing stability-in-distribution criteria are not applicable by these two examples.

AB - In this paper we investigate the stability in distribution for a class of stochastic functional differential equations (SFDEs), which include stochastic differential delay equations (SDDEs). Although stability in distribution has been studied by several authors recently, there is so far no stability-in-distribution criterion on SFDEs where the terms involved the delay components are highly nonlinear (not bounded by linear functions). In this paper we will establish the sufficient criteria on the stability in distribution for a class of highly nonlinear SFDEs. Two examples will be given to illustrate our new results. We also explain the reason why the existing stability-in-distribution criteria are not applicable by these two examples.

KW - stochastic functional differential equations

KW - stability in distribution

KW - Ito formula

KW - Brownian motion

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

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DO - 10.1016/j.sysconle.2019.104513

M3 - Article

SN - 0167-6911

VL - 132

SP - 1

EP - 10

JO - Systems and Control Letters

JF - Systems and Control Letters

M1 - 104513

ER -

Stability in distribution of stochastic functional differential equations

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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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Stability in distribution of stochastic functional differential equations

Abstract

Keywords

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Projects

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

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