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In the context of controlled differential equations, the signature is the exponential function on paths.
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P. Friz, N. Victoir, Multidimensional stochastic processes as rough paths
2010
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B. Hambly, T. Lyons, Uniqueness for the signature of a path of bounded variation and the reduced path group, Ann. of Math
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T. Cass, B. Driver, N. Lim, C. Litterer, On the integration of weakly geometric rough paths, to appear in the Journal of Mathematical Society of Japan
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2014
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T. Lyons, W. Xu, Inverting the signature of a path, arXiv:1406.7833, 2014
2014
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