40
IRUS TotalDownloads
Altmetric
A combinatorial approach to geometric rough paths and their controlled paths
File | Description | Size | Format | |
---|---|---|---|---|
2112.08034v1.pdf | Working Paper | 656.76 kB | Adobe PDF | View/Open |
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 |