Basic theory and stability analysis for neutral stochastic functional differential equations with pure jumps

Mengling Li, Feiqi Deng, Xuerong Mao

Research output: Contribution to journalArticle

1 Citation (Scopus)

Abstract

This paper investigates the existence and uniqueness of solutions to neutral stochastic functional differential equations with pure jumps (NSFDEwPJs). The boundedness and almost sure exponential stability are also considered. In general, the classical existence and uniqueness theorem of solutions can be obtained under a local Lipschitz condition and linear growth condition. However, there are many equations that do not obey the linear growth condition. Therefore, our first aim is to establish new theorems where the linear growth condition is no longer required whereas the upper bound for the diffusion operator will play a leading role. Moreover, the pth moment boundedness and almost sure exponential stability are also obtained under some loose conditions. Finally, we present two examples to illustrate the effectiveness of our results.
Original languageEnglish
Article number12204
Number of pages15
JournalScience in China Series F - Information Sciences
Volume62
Early online date16 Oct 2018
DOIs
Publication statusPublished - 31 Jan 2019

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Stochastic Functional Differential Equations
Neutral Functional Differential Equation
Growth Conditions
Almost Sure Exponential Stability
Stability Analysis
Jump
Differential equations
Asymptotic stability
Boundedness
Existence and Uniqueness Theorem
Lipschitz condition
Existence and Uniqueness of Solutions
Upper bound
Moment
Operator
Theorem

Keywords

  • neutral term
  • stochastic functional differential equations
  • pure jumps
  • existence and uniqueness theorem
  • stability analysis

Cite this

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abstract = "This paper investigates the existence and uniqueness of solutions to neutral stochastic functional differential equations with pure jumps (NSFDEwPJs). The boundedness and almost sure exponential stability are also considered. In general, the classical existence and uniqueness theorem of solutions can be obtained under a local Lipschitz condition and linear growth condition. However, there are many equations that do not obey the linear growth condition. Therefore, our first aim is to establish new theorems where the linear growth condition is no longer required whereas the upper bound for the diffusion operator will play a leading role. Moreover, the pth moment boundedness and almost sure exponential stability are also obtained under some loose conditions. Finally, we present two examples to illustrate the effectiveness of our results.",
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Basic theory and stability analysis for neutral stochastic functional differential equations with pure jumps. / Li, Mengling ; Deng, Feiqi; Mao, Xuerong.

In: Science in China Series F - Information Sciences, Vol. 62, 12204, 31.01.2019.

Research output: Contribution to journalArticle

TY - JOUR

T1 - Basic theory and stability analysis for neutral stochastic functional differential equations with pure jumps

AU - Li, Mengling

AU - Deng, Feiqi

AU - Mao, Xuerong

PY - 2019/1/31

Y1 - 2019/1/31

N2 - This paper investigates the existence and uniqueness of solutions to neutral stochastic functional differential equations with pure jumps (NSFDEwPJs). The boundedness and almost sure exponential stability are also considered. In general, the classical existence and uniqueness theorem of solutions can be obtained under a local Lipschitz condition and linear growth condition. However, there are many equations that do not obey the linear growth condition. Therefore, our first aim is to establish new theorems where the linear growth condition is no longer required whereas the upper bound for the diffusion operator will play a leading role. Moreover, the pth moment boundedness and almost sure exponential stability are also obtained under some loose conditions. Finally, we present two examples to illustrate the effectiveness of our results.

AB - This paper investigates the existence and uniqueness of solutions to neutral stochastic functional differential equations with pure jumps (NSFDEwPJs). The boundedness and almost sure exponential stability are also considered. In general, the classical existence and uniqueness theorem of solutions can be obtained under a local Lipschitz condition and linear growth condition. However, there are many equations that do not obey the linear growth condition. Therefore, our first aim is to establish new theorems where the linear growth condition is no longer required whereas the upper bound for the diffusion operator will play a leading role. Moreover, the pth moment boundedness and almost sure exponential stability are also obtained under some loose conditions. Finally, we present two examples to illustrate the effectiveness of our results.

KW - neutral term

KW - stochastic functional differential equations

KW - pure jumps

KW - existence and uniqueness theorem

KW - stability analysis

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DO - 10.1007/s11432-017-9302-9

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JO - Science in China Series F - Information Sciences

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