G-Lévy processes under sublinear expectations

Mingshang Hu; Shige Peng

doi:10.3934/puqr.2021001

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2021, Volume 6, Issue 1: 1-22. Doi: 10.3934/puqr.2021001

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G-Lévy processes under sublinear expectations

Mingshang Hu^1, and
Shige Peng^2, ,

1.
Zhongtai Securities Institute for Financial Studies, Shandong University, Jinan 250100, Shandong, China
2.
School of Mathematics, Shandong University, Jinan 250100, Shandong, China

Email: humingshang@sdu.edu.cn, peng@sdu.edu.cn
Email: humingshang@sdu.edu.cn, peng@sdu.edu.cn

Received: June 21, 2020

Accepted: December 13, 2020

Published: March 2021

This work was supported by National Key R&D Program of China (Grant No. 2018YFA0703900), National Natural Science Foundation of China (Grant No. 11671231) , Tian Yuan Fund of the National Natural Science Foundation of China (Grant Nos. 11526205 and 11626247) and National Basic Research Program of China (973 Program) (Grant No. 2007CB814900).

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Abstract

We introduce G-Lévy processes which develop the theory of processes with independent and stationary increments under the framework of sublinear expectations. We then obtain the Lévy–Khintchine formula and the existence for G-Lévy processes. We also introduce G-Poisson processes.

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Mathematics Subject Classification: 60H10; 60J60; 60J65.

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References

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