Abstract
In this paper, we study the averaging principle for neutral stochastic functional differential equations (SFDEs) with Poisson random measure. By stochastic inequality, Burkholder-Davis-Gundy’s inequality and Kunita’s inequality, we prove that the solution of the averaged neutral SFDEs with Poisson random measure converges to that of the standard one in (Formula presented.) sense and also in probability. Some illustrative examples are presented to demonstrate this theory.
| Language | English |
|---|---|
| Article number | 77 |
| Number of pages | 18 |
| Journal | Advances in Difference Equations |
| Volume | 2016 |
| Issue number | 1 |
| DOIs | |
| Publication status | Published - 15 Mar 2016 |
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Keywords
- averaging principle
- convergence in probability
- L convergence
- neutral SFDEs
- Poisson random measure
Cite this
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An averaging principle for neutral stochastic functional differential equations driven by Poisson random measure. / Mao, Wei; Mao, Xuerong.
In: Advances in Difference Equations, Vol. 2016, No. 1, 77, 15.03.2016.Research output: Contribution to journal › Article
TY - JOUR
T1 - An averaging principle for neutral stochastic functional differential equations driven by Poisson random measure
AU - Mao, Wei
AU - Mao, Xuerong
PY - 2016/3/15
Y1 - 2016/3/15
N2 - In this paper, we study the averaging principle for neutral stochastic functional differential equations (SFDEs) with Poisson random measure. By stochastic inequality, Burkholder-Davis-Gundy’s inequality and Kunita’s inequality, we prove that the solution of the averaged neutral SFDEs with Poisson random measure converges to that of the standard one in (Formula presented.) sense and also in probability. Some illustrative examples are presented to demonstrate this theory.
AB - In this paper, we study the averaging principle for neutral stochastic functional differential equations (SFDEs) with Poisson random measure. By stochastic inequality, Burkholder-Davis-Gundy’s inequality and Kunita’s inequality, we prove that the solution of the averaged neutral SFDEs with Poisson random measure converges to that of the standard one in (Formula presented.) sense and also in probability. Some illustrative examples are presented to demonstrate this theory.
KW - averaging principle
KW - convergence in probability
KW - L convergence
KW - neutral SFDEs
KW - Poisson random measure
UR - http://www.scopus.com/inward/record.url?scp=84961239326&partnerID=8YFLogxK
UR - http://advancesindifferenceequations.springeropen.com/articles/10.1186/s13662-016-0802-x
U2 - 10.1186/s13662-016-0802-x
DO - 10.1186/s13662-016-0802-x
M3 - Article
VL - 2016
JO - Advances in Difference Equations
T2 - Advances in Difference Equations
JF - Advances in Difference Equations
SN - 1687-1839
IS - 1
M1 - 77
ER -