# American Institute of Mathematical Sciences

September  2019, 24(9): 4937-4954. doi: 10.3934/dcdsb.2019039

## 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

Received  May 2018 Revised  July 2018 Published  February 2019

Fund Project: 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).

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.

Citation: Wei Mao, Liangjian Hu, Surong You, Xuerong Mao. The averaging method for multivalued SDEs with jumps and non-Lipschitz coefficients. Discrete & Continuous Dynamical Systems - B, 2019, 24 (9) : 4937-4954. doi: 10.3934/dcdsb.2019039
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