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.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Copyright information
© 2014 Springer International Publishing Switzerland
About this chapter
Cite this chapter
Friz, P.K., Hairer, M. (2014). Solutions to rough differential equations. In: A Course on Rough Paths. Universitext. Springer, Cham. https://doi.org/10.1007/978-3-319-08332-2_8
Download citation
DOI: https://doi.org/10.1007/978-3-319-08332-2_8
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-08331-5
Online ISBN: 978-3-319-08332-2
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)