Abstract
We identify the solution to a rough differential equation driven by the Ito or Stratonovich lift of Brownian motion with the solution to the corresponding stochastic differential equation. In combination with continuity of the Ito-Lyons maps, a quick proof of the Wong-Zakai theorem is given. Applications to Stroock-Varadhan support theory and Freidlin-Wentzell large deviations are briefly discussed.
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© 2014 Springer International Publishing Switzerland
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Friz, P.K., Hairer, M. (2014). Stochastic differential equations. In: A Course on Rough Paths. Universitext. Springer, Cham. https://doi.org/10.1007/978-3-319-08332-2_9
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DOI: https://doi.org/10.1007/978-3-319-08332-2_9
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Publisher Name: Springer, Cham
Print ISBN: 978-3-319-08331-5
Online ISBN: 978-3-319-08332-2
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