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- W2080353622 abstract "In this article we consider rough differential equations (RDEs) driven by non-geometric rough paths, using the concept of branched rough paths introduced in Gubinelli (2004). We first show that branched rough paths can equivalently be defined as $gamma$-Holder continuous paths in some Lie group, akin to geometric rough paths. We then show that every branched rough path can be encoded in a geometric rough path. More precisely, for every branched rough path $mathbf{X}$ lying above a path $X$, there exists a geometric rough path $bar{mathbf{X}}$ lying above an extended path $bar X$, such that $bar{mathbf{X}}$ contains all the information of $mathbf{X}$. As a corollary of this result, we show that every RDE driven by a non-geometric rough path $mathbf{X}$ can be rewritten as an extended RDE driven by a geometric rough path $bar{mathbf{X}}$. One could think of this as a generalisation of the It^o-Stratonovich correction formula." @default.
- W2080353622 created "2016-06-24" @default.
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- W2080353622 date "2012-10-23" @default.
- W2080353622 modified "2023-09-27" @default.
- W2080353622 title "Geometric versus non-geometric rough paths" @default.
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