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arXiv · 1807.05692

On SDEs with Lipschitz coefficients, driven by continuous, model-free martingales

Lesiba Ch. Galane·Rafał M. Łochowski·Farai J. Mhlanga
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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.

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Lesiba Ch. Galane, Rafał M. Łochowski, Farai J. Mhlanga. 2022-02-14. On SDEs with Lipschitz coefficients, driven by continuous, model-free martingales. https://arxiv.org/abs/1807.05692

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