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

Wei Mao; Liangjian Hu; Surong You; Xuerong Mao

doi:10.3934/dcdsb.2019039

Article Contents

2019, Volume 24, Issue 9: 4937-4954. Doi: 10.3934/dcdsb.2019039

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

1.
College of Information Sciences and Technology, Donghua University, Shanghai, 201620, China
2.
School of mathematics and information technology, Jiangsu Second Normal University, Nanjing, 210013, China
3.
Department of Applied Mathematics, Donghua University, Shanghai 201620, China
4.
Department of Mathematics and Statistics, University of Strathclyde, Glasgow G1 1XH, U.K

^* Corresponding author: Liangjian Hu
^* Corresponding author: Liangjian Hu

Received: May 2018

Revised: July 2018

Early access: February 2019

Published: July 2019

The research of W.Mao was supported by the National Natural Science Foundation of China (11401261) and "333 High-level Project" of Jiangsu Province. The research of L.Hu was supported by the National Natural Science Foundation of China (11471071). The research of S.You was supported by the Natural Science Foundation of Shanghai (17ZR1401300). The research of X.Mao was supported by the Leverhulme Trust (RF-2015-385), the Royal Society (WM160014, Royal Society Wolfson Research Merit Award), the Royal Society and the Newton Fund (NA160317, Royal Society-Newton Advanced Fellowship), the EPSRC (EP/K503174/1).

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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.

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Mathematics Subject Classification: Primary: 60H10, 34C29.

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