Abstract
We prove the existence and uniqueness of solutions of SDEs with Lipschitz coefficients, driven by continuous, model-free martingales. The main tool in our reasoning is Picard’s iterative procedure and a model-free version of the Burkholder-Davis-Gundy inequality for integrals driven by model-free, continuous martingales. We work with a new outer measure which assigns zero value exactly to those properties which are instantly blockable.
Funding Statement
The work of Lesiba Ch. Galane and Farai J. Mhlanga was supported in part by the National Research Foundation of South Africa (Grant Number: 105924). The work of Rafał M. Łochowski was partially funded by the National Science Centre, Poland, under Grant No. B/STand Grant No. B/ST.
Acknowledgments
Part of this work was done while R.M. Łochowski was visiting the University of Limpopo. The warm hospitality of the University of Limpopo is gratefully acknowledged. The authors are grateful to Vladimir Vovk and Adam Osękowski for valuable questions and comments.
Citation
Lesiba Ch. Galane. Rafał M. Łochowski. Farai J. Mhlanga. "On SDEs with Lipschitz coefficients, driven by continuous, model-free martingales." Electron. Commun. Probab. 28 1 - 12, 2023. https://doi.org/10.1214/23-ECP520
Information
