Signatures of rough paths

Discrete representation of continuous signals and converse



I am not sure yet. Some kind of encoding of signals which is somewhere between sampling theory, rough SDEs and integral transforms.

References

Bonnier, Patric, Patrick Kidger, Imanol Perez Arribas, Cristopher Salvi, and Terry Lyons. 2019. “Deep Signature Transforms.” In Advances in Neural Information Processing Systems. Vol. 32. Curran Associates, Inc. http://arxiv.org/abs/1905.08494.
Chevyrev, Ilya, and Andrey Kormilitzin. 2016. “A Primer on the Signature Method in Machine Learning.” March 11, 2016. http://arxiv.org/abs/1603.03788.
Kalsi, Jasdeep, Terry Lyons, and Imanol Perez Arribas. 2020. “Optimal Execution with Rough Path Signatures.” SIAM Journal on Financial Mathematics 11 (2): 470–93. https://doi.org/10.1137/19M1259778.
Kelly, David. 2016. “Rough Path Recursions and Diffusion Approximations.” The Annals of Applied Probability 26 (1). https://doi.org/10.1214/15-AAP1096.
Lyons, Terry. 1994. “Differential Equations Driven by Rough Signals (I): An Extension of an Inequality of L. C. Young.” Mathematical Research Letters 1 (4): 451–64. https://doi.org/10.4310/MRL.1994.v1.n4.a5.
———. 2014. “Rough Paths, Signatures and the Modelling of Functions on Streams.” May 18, 2014. http://arxiv.org/abs/1405.4537.
Lyons, Terry J, and Nadia Sidorova. n.d. “Sound Compression – a Rough Path Approach,” 6.

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