Understand
We explain the algebra needed to make sense of the log signature of a path, with plenty of examples.
- We show how the log signature can be calculated numerically, and explain some software tools which demonstrate it.
Built on
“A basis for free Lie rings and higher commutators in free groups”, 1950
Marshall Hall · 1950
Earlier work this paper cites.
“Integration of Paths – A Faithful Representation of Paths by Noncommutative Formal Power Series”
Kuo-Tsai Chen · 1958
Earlier work this paper cites.
“Free Lie Algebras”, 1994
Christophe Reutenauer · 1994
Earlier work this paper cites.
“Standard Lyndon Bases of Lie Algebras and Enveloping Algebras”
Pierre Lalonde and Arun Ram · 1995
Earlier work this paper cites.
Similar
“Uniqueness for the signature of a path of bounded variation and the reduced path group”, 2005
Ben Hambly and Terry Lyons · 2005
Cited alongside, same era.
“Differential Equations Driven by Rough Paths”, 2007
Terry Lyons, Michael Caruana and Thierry Lévy · 2007
Cited alongside, same era.
Fernando Casas and Ander Murua · 2009
Cited alongside, same era.
“The BCH formula and the symmetric BCH formula up to terms of degree 20”
Fernando Casas and Ander Murua
Cited in the paper.
Then
“CoRoPa Computational Rough Paths (software library)”, 2010
Terry Lyons et al · 2010
Later among the works it cites.
“Necklace polynomial”, 2015
Wikipedia · 2015
Later among the works it cites.
“A Primer on the Signature Method in Machine Learning”, 2016
Ilya Chevyrev and Andrey Kormilitzin · 2016
Later among the works it cites.
Beyond the bibliography
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