Abstract
At first sight, the notation R Y dX introduced in Chapter 4 is ambiguous since the resulting controlled rough path depends in general on the choices of both the secondorder process X and the derivative process Y 0 . Fortunately, this “lack of completeness” in our notations is mitigated by the fact that in virtually all situations of interest, Y is constructed by using a small number of elementary operations described in this chapter. For all of these operations, it turns out to be intuitively rather clear how the corresponding derivative process is constructed.
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Friz, P.K., Hairer, M. (2020). Operations on controlled rough paths. In: A Course on Rough Paths. Universitext. Springer, Cham. https://doi.org/10.1007/978-3-030-41556-3_7
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DOI: https://doi.org/10.1007/978-3-030-41556-3_7
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