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Title: Effective algorithms for inverting the signature of a path
Author: Chang, Jiawei
Awarding Body: University of Oxford
Current Institution: University of Oxford
Date of Award: 2018
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The signature of a path is an important concept in rough paths theory. It has been proved in the literature that the terms in the signature of a path are bounded above, and it would then be interesting to consider whether a lower bound exists for the signature of a bounded-variation path. It has also been proved that the signature of a bounded-variation path is unique up to some modifications, then a natural question is reconstructing the path from its signature, i.e. inverting the signature of a path. We show the connection between the two questions above, and provide practical methods for signature inversion. First we prove a result about the super-multiplicativity and the decay of the signature of a path with bounded variation, then we describe the method of symmetrisation, which was first introduced by Lyons and Xu, and demonstrate an algorithm to invert the signature of a monotone path. Moreover we introduce the method of inverting the signature by insertion, and provide examples using the insertion method to invert the signature of a path. We compare these two methods of signature inversion, and illustrate the differences with computational results.
Supervisor: Lyons, Terry ; Ni, Hao Sponsor: Not available
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID:  DOI: Not available
Keywords: Mathematics