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Rough path theory is focused on capturing and making precise the interactions between highly oscillatory and non-linear systems.
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Wei-Liang Chow, Über Systeme von linearen partiellen Differentialgleichungen erster Ordnung , Math. Ann. 117
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Kuo-Tsai Chen, Integration of paths, geometric invariants and a generalized Baker-Hausdorff formula , Ann. of Math. (2) 65
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Nicolas Bourbaki, Lie groups and Lie algebras. Chapters 1–3 , Elements of Mathematics (Berlin), Springer-Verlag, Berlin, 1989, Translated from the French, Reprint of the 1975 edition. MR 979493 (89k:17001)
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Fabienne Castell and Jessica Gaines, An efficient approximation method for stochastic differential equations by means of the exponential lie series , Mathematics and computers in simulation 38
1995
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Thomas Fawcett, Problems in stochastic analysis: Connections between rough paths and non-commutative harmonic analysis , Ph.D. thesis, University of Oxford, 2002
2002
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Terry J. Lyons and Nadia Sidorova, On the radius of convergence of the logarithmic signature , Illinois J. Math. 50
2006
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Terry J Lyons, Michael Caruana, and Thierry Lévy, Differential equations driven by rough paths , Springer, 2007
2007
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Peter K Friz and Nicolas B Victoir, Multidimensional stochastic processes as rough paths: theory and applications , vol. 120, Cambridge University Press, 2010
2010
Cited alongside, same era.
Ben Hambly and Terry Lyons, Uniqueness for the signature of a path of bounded variation and the reduced path group , Ann. of Math.(2) 171
2010
Cited alongside, same era.
Christian Litterer and Terry Lyons, Cubature on wiener space continued , Stochastic Processes and Applications to Mathematical Finance (2011), 197–218
2011
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2011
Cited alongside, same era.
2013
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Terry J Lyons and Danyu Yang, The partial sum process of orthogonal expansions as geometric rough process with fourier series as an example—an improvement of menshov–rademacher theorem , Journal of Functional Analysis 265
2013
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2013
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2014
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2013
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2013
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2013
Cited alongside, same era.
Martin Hairer and Natesh S Pillai, Regularity of laws and ergodicity of hypoelliptic sdes driven by rough paths , The Annals of Probability 41
2013
Cited alongside, same era.
Thomas Cass and Terry Lyons, Evolving communities with individual preferences , 1303.4243 to appear in Proceedings of London Mathematical Society (2014), 1–21
2014
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2014
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Martin Hairer, A theory of regularity structures , Invent. Math. (2014)
2014
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Terry Lyons and Nicolas Victoir, Cubature on wiener space , Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences 460
2041
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