15 citations · 56 across the 22 of their papers we have counts for
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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★ 2 cited
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…
math.AP2018★ 1 cited
Long Time Asymptotics of Heat Kernels and Brownian Winding Numbers on Manifolds with Boundary
Xi Geng, Gautam Iyer
Let M be a compact Riemannian manifold with smooth boundary. We obtain the exact long time asymptotic behaviour of the heat kernel on abelian coverings of M with mixed Dirichlet an…