Stability in distribution of stochastic functional differential equations

Ya Wang, Fuke Wu, Xuerong Mao

Research output: Contribution to journalArticle

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.
LanguageEnglish
Number of pages22
JournalSystems and Control Letters
Publication statusAccepted/In press - 23 Jul 2019

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Stochastic Functional Differential Equations
Differential equations
Stochastic Differential Delay Equations
Linear Function
Sufficient
Term

Keywords

  • stochastic functional differential equations
  • stability in distribution
  • Ito formula
  • Brownian motion

Cite this

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Stability in distribution of stochastic functional differential equations. / Wang, Ya; Wu, Fuke; Mao, Xuerong.

In: Systems and Control Letters, 23.07.2019.

Research output: Contribution to journalArticle

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AU - Wang, Ya

AU - Wu, Fuke

AU - Mao, Xuerong

PY - 2019/7/23

Y1 - 2019/7/23

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

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M3 - Article

JO - Systems and Control Letters

T2 - Systems and Control Letters

JF - Systems and Control Letters

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