1 citations · 1 across the 6 of their papers we have counts for
6 papers
Orthogonal polynomials on path-space
Ilya Chevyrev, Emilio Ferrucci, Darrick Lee +3
We consider the orthogonalisation of the signature of a stochastic process as the analogue of orthogonal polynomials on path-space. Under an infinite radius of convergence assumpti…
Thin homotopy and the signature of piecewise linear surfaces
Francis Bischoff, Darrick Lee
We introduce a crossed module of piecewise linear surfaces and study the signature homomorphism, defined as the surface holonomy of a universal translation invariant -connection…
Path-Dependent SDEs: Solutions and Parameter Estimation
Pardis Semnani, Vincent Guan, Elina Robeva +1
We develop a consistent method for estimating the parameters of a rich class of path-dependent SDEs, called signature SDEs, which can model general path-dependent phenomena. Path s…
Communities in the Kuramoto Model: Dynamics and Detection via Path Signatures
Tâm Johan Nguyên, Darrick Lee, Bernadette Jana Stolz
The behavior of multivariate dynamical processes is often governed by underlying structural connections that relate the components of the system. For example, brain activity, which…
The Surface Signature and Rough Surfaces
Darrick Lee
Parallel transport, or path development, provides a rich characterization of paths which preserves the underlying algebraic structure of concatenation. The path signature is univer…
Random Surfaces and Higher Algebra
Darrick Lee, Harald Oberhauser
We introduce a characteristic function for laws of random surfaces , in the spirit of expected path developments for one-dimensiona…