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A combinatorial approach to geometric rough paths and their controlled paths

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Title: A combinatorial approach to geometric rough paths and their controlled paths
Authors: Cass, T
Driver, BK
Litterer, C
Ferrucci, ER
Item Type: Working Paper
Abstract: We develop the structure theory for transformations of weakly geometric rough paths of bounded $1 < p$-variation and their controlled paths. Our approach differs from existing approaches as it does not rely on smooth approximations. We derive an explicit combinatorial expression for the rough path lift of a controlled path, and use it to obtain fundamental identities such as the associativity of the rough integral, the adjunction between pushforwards and pullbacks, and a change of variables formula for rough differential equations (RDEs). As applications we define rough paths, rough integration and RDEs on manifolds, extending the results of [CDL15] to the case of arbitrary $p$.
Issue Date: 26-Jan-2022
URI: http://hdl.handle.net/10044/1/94264
Publisher: ArXiv
Copyright Statement: ©2022 The Author(s)
Sponsor/Funder: Engineering & Physical Science Research Council (E
Funder's Grant Number: BKR01300
Keywords: math.CA
math.CA
60L20
math.CA
math.CA
60L20
Publication Status: Published
Appears in Collections:Financial Mathematics
Mathematics