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The signature of a path can be described as its full non-commutative exponential.
1903
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2012
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T. Lyons, Rough paths, signatures and the modelling of functions on streams , Proceedings of the International Congress of Mathematicians—Seoul 2014. Vol. IV, Kyung Moon Sa, Seoul, 2014, pp. 163–184. MR 3727607
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T. Lyons and H. Ni, Expected signature of brownian motion up to the first exit time from a bounded domain , Ann. Probab. 43
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2003
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2006
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I. Chevyrev and T. Lyons, Characteristic functions of measures on geometric rough paths , Ann. Probab. 44
2016
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P. K. Friz and A. Shekhar, General rough integration, Lévy rough paths and a Lévy–Kintchine-type formula , Ann. Probab. 45
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2018
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2019
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I. Chevyrev and P. K. Friz, Canonical rdes and general semimartingales as rough paths , Ann. Probab. 47
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J. Gatheral and M. Keller-Ressel, Affine forward variance models , Finance Stoch. 23
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E. Alos, J. Gatheral, and R. Radoičić, Exponentiation of conditional expectations under stochastic volatility , Quantitative Finance; SSRN (2017) 20
2020
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Y. Bruned, C. Curry, and K. Ebrahimi-Fard, Quasi-shuffle algebras and renormalisation of rough differential equations , Bulletin of the London Mathematical Society 52
2020
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P. Bonnier and H. Oberhauser, Signature cumulants, ordered partitions, and independence of stochastic processes , Bernoulli 26
2020
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P. K. Friz and M. Hairer, A course on rough paths , 2nd ed., Universitext, Springer International Publishing, 2020
2020
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T. Lyons and N. 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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