An averaging principle for neutral stochastic functional differential equations driven by Poisson random measure

Wei Mao, Xuerong Mao

Research output: Contribution to journalArticle

1 Citation (Scopus)

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.

LanguageEnglish
Article number77
Number of pages18
JournalAdvances in Difference Equations
Volume2016
Issue number1
DOIs
Publication statusPublished - 15 Mar 2016

Fingerprint

Averaging Principle
Poisson Random Measure
Stochastic Functional Differential Equations
Neutral Functional Differential Equation
Differential equations
Converge
Demonstrate

Keywords

  • averaging principle
  • convergence in probability
  • L convergence
  • neutral SFDEs
  • Poisson random measure

Cite this

@article{4fa70423c2374699a81d29456031d1c9,
title = "An averaging principle for neutral stochastic functional differential equations driven by Poisson random measure",
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.",
keywords = "averaging principle, convergence in probability, L convergence, neutral SFDEs, Poisson random measure",
author = "Wei Mao and Xuerong Mao",
year = "2016",
month = "3",
day = "15",
doi = "10.1186/s13662-016-0802-x",
language = "English",
volume = "2016",
journal = "Advances in Difference Equations",
issn = "1687-1839",
number = "1",

}

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 -