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

Haoyi Mo; Mengling Li; Feiqi Deng; Xuerong Mao

doi:10.1007/s11432-017-9301-y

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

Haoyi Mo, Mengling Li, Feiqi Deng, Xuerong Mao

Mathematics And Statistics

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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 language	English
Article number	70214
Number of pages	15
Journal	Science in China Series F - Information Sciences
Volume	61
Issue number	7
DOIs	https://doi.org/10.1007/s11432-017-9301-y
Publication status	Published - 4 Jun 2018

Keywords

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

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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.",

keywords = "neutral stochastic functional differential equations with jumps, almost sure exponential stability, mean-square exponential stability, Euler-Maruyama method",

author = "Haoyi Mo and Mengling Li and Feiqi Deng and Xuerong Mao",

note = "{\textcopyright} Science China Press and Springer-Verlag GmbH Germany, part of Springer Nature 2018 Mo, H., Li, M., Deng, F. et al. Exponential stability of the Euler-Maruyama method for neutral stochastic functional differential equations with jumps. Sci. China Inf. Sci. 61, 70214 (2018). https://doi.org/10.1007/s11432-017-9301-y",

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T1 - Exponential stability of the Euler-Maruyama method for neutral stochastic functional differential equations with jumps

AU - Mo, Haoyi

AU - Li, Mengling

AU - Deng, Feiqi

AU - Mao, Xuerong

N1 - © Science China Press and Springer-Verlag GmbH Germany, part of Springer Nature 2018 Mo, H., Li, M., Deng, F. et al. Exponential stability of the Euler-Maruyama method for neutral stochastic functional differential equations with jumps. Sci. China Inf. Sci. 61, 70214 (2018). https://doi.org/10.1007/s11432-017-9301-y

PY - 2018/6/4

Y1 - 2018/6/4

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

SN - 1009-2757

VL - 61

JO - Science in China Series F - Information Sciences

JF - Science in China Series F - Information Sciences

IS - 7

M1 - 70214

ER -

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

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Keywords

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