Learning from the past, predicting the statistics for the future, learning an evolving system

Integration of paths, geometric invariants and a generalized baker-hausdorff formula

Kuo-Tsai Chen · 1957

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Iterated path integrals

Kuo-Tsai Chen · 1977

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The maximum rate of convergence of discrete approximations for stochastic differential equations

J Clark and R Cameron · 1980

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Modelling the coherence in short-run nominal exchange rates: a multivariate generalized arch model

Tim Bollerslev · 1990

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Applied nonparametric regression

Wolfgang Hardle · 1990

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Differential equations driven by rough signals

Terry J Lyons · 1998

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System control and rough paths

Terry Lyons and Zhongmin Qian · 2002

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Problems in stochastic analysis: connections between rough paths and noncommutative harmonic analysis

T. Fawcett · 2003

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A new class of wavelet networks for nonlinear system identification

Stephen Billings, Hua-Liang Wei, et al · 2005

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Differential Equation driven by Rough Paths

Terry Lyons, Thierry L e ´ \acute{e} vy, and Michael Caruana · 2006

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Gaussian Processes for Machine Learning

C. E. Rasmussen and C. K. I. Williams · 2006

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Optimal approximation of the second iterated integral of brownian motion

Andrew S Dickinson · 2007

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Euler estimates for rough differential equations

Peter Friz and Nicolas Victoir · 2008

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Uniqueness for the signature of a path of bounded variation and the reduced path group

B.M. Hambly and Terry Lyons · 2010

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Parameter estimation for rough differential equations

Anastasia Papavasiliou, Christophe Ladroue, et al · 2011

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A Course on Rough Paths: With an Introduction to Regularity Structures

Peter K Friz and Martin Hairer · 2014

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A feature set for streams and an application to high-frequency financial tick data

Terry Lyons, Hao Ni, and Harald Oberhauser · 2014

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The uniqueness of signature problem in the non-markov setting

Horatio Boedihardjo and Xi Geng · 2015

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Uniform factorial decay estimates for controlled differential equations

Horatio Boedihardjo, Terry Lyons, and Danyu Yang · 2015

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Characteristic functions of measures on geometric rough paths

Ilya Chevyrev and Terry Lyons · 2015

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Physical brownian motion in a magnetic field as a rough path

Peter Friz, Paul Gassiat, and Terry Lyons · 2015

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