Path independence of the additive functionals for stochastic differential equations driven by G-lévy processes

Huijie Qiao; Jiang-Lun Wu

doi:10.3934/puqr.2022007

Article Contents

2022, Volume 7, Issue 2: 101-118. Doi: 10.3934/puqr.2022007

This issue Previous Article A note on the cluster set of the law of the iterated logarithm under sub-linear expectations Next Article Harnack inequality and gradient estimate for functional G-SDEs with degenerate noise

Path independence of the additive functionals for stochastic differential equations driven by G-lévy processes

Huijie Qiao^1,2, , and
Jiang-Lun Wu^3,

1.
School of Mathematics, Southeast University, Nanjing 211189, Jiangsu, China
2.
Department of Mathematics, University of Illinois at Urbana-Champaign, Urbana, IL 61801, USA
3.
Department of Mathematics, Computational Foundry, Swansea University, Bay Campus, Swansea SA1 8EN, UK

hjqiaogean@seu.edu.cn
hjqiaogean@seu.edu.cn

Received: January 30, 2022

Accepted: May 29, 2022

Early access: June 2022

Published: June 2022

The first author thanks Professor Renming Song for providing her an excellent environment to work in the University of Illinois at Urbana-Champaign. She also thanks Professor Hongjun Gao for valuable discussion. Both authors are grateful to the referees for their constructive suggestions and comments which led to improve the results and the presentation of this paper. This work was partly supported by NSF of China (Grant Nos. 11001051, 11371352, 12071071) and China Scholarship Council (Grant No. 201906095034)..

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Abstract

In this study, we are interested in stochastic differential equations driven by G-Lévy processes. We illustrate that a certain class of additive functionals of the equations of interest exhibits the path-independent property, generalizing a few known findings in the literature. The study is ended with many examples.

Keywords:

The path independence,
Additive functionals,
G-Lévy processes,
Stochastic differential equations driven by G-Lévy processes.

Mathematics Subject Classification: 60H10, 60G51.

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References

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