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math.CA2020★ 2 cited
Lipschitz-stability of Controlled Rough Paths and Rough Differential Equations
Horatio Boedihardjo, Xi Geng
We provide an account for the existence and uniqueness of solutions to rough differential equations under the framework of controlled rough paths. The case when the driving path is…
math.CA2018
Path Developments and Tail Asymptotics of Signature for Pure Rough Paths
Horatio Boedihardjo, Xi Geng, Nikolaos P. Souris
Solutions to linear controlled differential equations can be expressed in terms of iterated path integrals of the driving path. This collection of iterated integrals encodes essent…
math.CA2018
A Non-vanishing Property for the Signature of a Path
Horatio Boedihardjo, Xi Geng
We prove that a continuous path with finite length in a real Banach space cannot have infinitely many zero components in its signature unless it is tree-like. In particular, this a…