Abstract
We show how to solve differential equations driven by rough paths by a simple Picard iteration argument. This yields a pathwise solution theory mimicking the standard solution theory for ordinary differential equations. We start with the simple case of differential equations driven by a signal that is sufficiently regular for Young’s theory of integration to apply and then proceed to the case of more general rough signals.
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Friz, P.K., Hairer, M. (2020). Solutions to rough differential equations. In: A Course on Rough Paths. Universitext. Springer, Cham. https://doi.org/10.1007/978-3-030-41556-3_8
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DOI: https://doi.org/10.1007/978-3-030-41556-3_8
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Publisher Name: Springer, Cham
Print ISBN: 978-3-030-41555-6
Online ISBN: 978-3-030-41556-3
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