13 citations · 63 across the 22 of their papers we have counts for
9 papers · 1 filter
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…
SL_2(R)-developments and Signature Asymptotics for Planar Paths with Bounded Variation
Horatio Boedihardjo, Xi Geng
The signature transform, defined by the formal tensor series of global iterated path integrals, is a homomorphism between the path space and the tensor algebra that has been studie…
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…
Factorial Decay of Iterated Rough Integrals
Horatio Boedihardjo
In this complementary note to [1] (arXiv:1501.05641), we provide an alternative proof for the factorial decay estimate of iterated integrals for geometric rough paths without using…
Note on the Signatures of Rough Paths in a Banach Space
Horatio Boedihardjo, Xi Geng, Terry Lyons +1
We prove some results, which are used in arXiv:1406.7871, about weakly geometric rough paths that are well-known in finite dimensions, but need proof in the infinite dimensional se…
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…
The Signature of a Rough Path: Uniqueness
Horatio Boedihardjo, Xi Geng, Terry Lyons +1
In the context of controlled differential equations, the signature is the exponential function on paths. B. Hambly and T. Lyons proved that the signature of a bounded variation pat…
Simple Piecewise Geodesic Interpolation of Simple and Jordan Curves with Applications
Horatio Boedihardjo, Xi Geng
We explicitly construct simple, piecewise minimizing geodesic, arbitrarily fine interpolation of simple and Jordan curves on a Riemannian manifold. In particular, a finite sequence…