The averaging method for multivalued SDEs with jumps and non-Lipschitz coefficients

Wei Mao, Liangjian Hu, Surong You, Xuerong Mao

Research output: Contribution to journalArticle

Abstract

In this paper, we study the averaging principle for multivalued SDEs with jumps and non-Lipschitz coefficients. By the Bihari’s inequality and the properties of the concave function, we prove that the solution of averaged multivalued SDE with jumps converges to that of the standard one in the sense of mean square and also in probability. Finally, two examples are presented to illustrate our theory.
LanguageEnglish
Number of pages19
JournalDiscrete and Continuous Dynamical Systems - Series B
Publication statusAccepted/In press - 3 Oct 2018

Fingerprint

Non-Lipschitz
Averaging Method
Multivalued
Jump
Averaging Principle
Concave function
Coefficient
Mean Square
Converge
Standards

Keywords

  • multivalued SDES
  • non-Lipschitz coefficients
  • averaging principle
  • poisson random measure

Cite this

@article{87bd164cd4a94ba2b86ae24a939d436d,
title = "The averaging method for multivalued SDEs with jumps and non-Lipschitz coefficients",
abstract = "In this paper, we study the averaging principle for multivalued SDEs with jumps and non-Lipschitz coefficients. By the Bihari’s inequality and the properties of the concave function, we prove that the solution of averaged multivalued SDE with jumps converges to that of the standard one in the sense of mean square and also in probability. Finally, two examples are presented to illustrate our theory.",
keywords = "multivalued SDES, non-Lipschitz coefficients, averaging principle, poisson random measure",
author = "Wei Mao and Liangjian Hu and Surong You and Xuerong Mao",
year = "2018",
month = "10",
day = "3",
language = "English",
journal = "Discrete and Continuous Dynamical Systems - Series B",
issn = "1531-3492",

}

The averaging method for multivalued SDEs with jumps and non-Lipschitz coefficients. / Mao, Wei; Hu, Liangjian; You, Surong; Mao, Xuerong.

In: Discrete and Continuous Dynamical Systems - Series B, 03.10.2018.

Research output: Contribution to journalArticle

TY - JOUR

T1 - The averaging method for multivalued SDEs with jumps and non-Lipschitz coefficients

AU - Mao, Wei

AU - Hu, Liangjian

AU - You, Surong

AU - Mao, Xuerong

PY - 2018/10/3

Y1 - 2018/10/3

N2 - In this paper, we study the averaging principle for multivalued SDEs with jumps and non-Lipschitz coefficients. By the Bihari’s inequality and the properties of the concave function, we prove that the solution of averaged multivalued SDE with jumps converges to that of the standard one in the sense of mean square and also in probability. Finally, two examples are presented to illustrate our theory.

AB - In this paper, we study the averaging principle for multivalued SDEs with jumps and non-Lipschitz coefficients. By the Bihari’s inequality and the properties of the concave function, we prove that the solution of averaged multivalued SDE with jumps converges to that of the standard one in the sense of mean square and also in probability. Finally, two examples are presented to illustrate our theory.

KW - multivalued SDES

KW - non-Lipschitz coefficients

KW - averaging principle

KW - poisson random measure

UR - http://www.aimsciences.org/journal/1531-3492

M3 - Article

JO - Discrete and Continuous Dynamical Systems - Series B

T2 - Discrete and Continuous Dynamical Systems - Series B

JF - Discrete and Continuous Dynamical Systems - Series B

SN - 1531-3492

ER -