Exponential stability of the Euler-Maruyama method for neutral stochastic functional differential equations with jumps

Haoyi Mo, Mengling Li, Feiqi Deng, Xuerong Mao

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Abstract

The exponential stability of trivial solution and the numerical solution for neutral stochastic functional differential equations (NSFDEs) with jumps is considered. The stability includes the almost sure exponential stability and the mean-square exponential stability. New conditions for jumps are proposed by means of the Borel measurable function to ensure stability. It is shown that if the drift coefficient satisfies the linear growth condition, the Euler-Maruyama method can reproduce the corresponding exponential stability of the trivial solution. A numerical example is constructed to illustrate our theory.
Original languageEnglish
JournalScience in China Series F - Information Sciences
DOIs
Publication statusAccepted/In press - 5 Dec 2017

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Euler-Maruyama Method
Stochastic Functional Differential Equations
Neutral Functional Differential Equation
Exponential Stability
Asymptotic stability
Jump
Differential equations
Trivial
Almost Sure Exponential Stability
Borel Functions
Mean-square Stability
Measurable function
Growth Conditions
Numerical Solution
Numerical Examples
Coefficient

Keywords

  • neutral stochastic functional differential equations with jumps
  • almost sure exponential stability
  • mean-square exponential stability
  • Euler-Maruyama method

Cite this

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title = "Exponential stability of the Euler-Maruyama method for neutral stochastic functional differential equations with jumps",
abstract = "The exponential stability of trivial solution and the numerical solution for neutral stochastic functional differential equations (NSFDEs) with jumps is considered. The stability includes the almost sure exponential stability and the mean-square exponential stability. New conditions for jumps are proposed by means of the Borel measurable function to ensure stability. It is shown that if the drift coefficient satisfies the linear growth condition, the Euler-Maruyama method can reproduce the corresponding exponential stability of the trivial solution. A numerical example is constructed to illustrate our theory.",
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AU - Mo, Haoyi

AU - Li, Mengling

AU - Deng, Feiqi

AU - Mao, Xuerong

PY - 2017/12/5

Y1 - 2017/12/5

N2 - The exponential stability of trivial solution and the numerical solution for neutral stochastic functional differential equations (NSFDEs) with jumps is considered. The stability includes the almost sure exponential stability and the mean-square exponential stability. New conditions for jumps are proposed by means of the Borel measurable function to ensure stability. It is shown that if the drift coefficient satisfies the linear growth condition, the Euler-Maruyama method can reproduce the corresponding exponential stability of the trivial solution. A numerical example is constructed to illustrate our theory.

AB - The exponential stability of trivial solution and the numerical solution for neutral stochastic functional differential equations (NSFDEs) with jumps is considered. The stability includes the almost sure exponential stability and the mean-square exponential stability. New conditions for jumps are proposed by means of the Borel measurable function to ensure stability. It is shown that if the drift coefficient satisfies the linear growth condition, the Euler-Maruyama method can reproduce the corresponding exponential stability of the trivial solution. A numerical example is constructed to illustrate our theory.

KW - neutral stochastic functional differential equations with jumps

KW - almost sure exponential stability

KW - mean-square exponential stability

KW - Euler-Maruyama method

U2 - 10.1007/s11432-017-9301-y

DO - 10.1007/s11432-017-9301-y

M3 - Article

JO - Science in China Series F - Information Sciences

JF - Science in China Series F - Information Sciences

SN - 1009-2757

ER -