2 citations · 2 across the 2 of their papers we have counts for
5 papers
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…
The expected signature of Brownian motion stopped on the boundary of a circle has finite radius of convergence
Horatio Boedihardjo, Joscha Diehl, Marc Mezzarobba +1
The expected signature is an analogue of the Laplace transform for rough paths. Chevyrev and Lyons showed that, under certain moment conditions, the expected signature determines t…
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…
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…
Uniform Factorial Decay Estimate for the Remainder of Rough Taylor Expansion
Horatio Boedihardjo, Danyu Yang, Terry Lyons
We establish an uniform factorial decay estimate for the Taylor approximation of solutions to controlled differential equations. Its proof requires a factorial decay estimate for c…