Effective algorithms for inverting the signature of a path
<p>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. I...
| Main Author: | |
|---|---|
| Other Authors: | |
| Format: | Thesis |
| Published: |
2018
|
| Subjects: |
| _version_ | 1811141027442982912 |
|---|---|
| author | Chang, J |
| author2 | Lyons, T |
| author_facet | Lyons, T Chang, J |
| author_sort | Chang, J |
| collection | OXFORD |
| description | <p>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. <em>inverting the signature of a path</em>.</p> <p>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.</p> |
| first_indexed | 2024-03-06T18:53:50Z |
| format | Thesis |
| id | oxford-uuid:11246a34-2c2b-40dd-be88-2a0b560fdfbf |
| institution | University of Oxford |
| last_indexed | 2024-09-25T04:31:21Z |
| publishDate | 2018 |
| record_format | dspace |
| spelling | oxford-uuid:11246a34-2c2b-40dd-be88-2a0b560fdfbf2024-08-29T08:37:53ZEffective algorithms for inverting the signature of a pathThesishttp://purl.org/coar/resource_type/c_db06uuid:11246a34-2c2b-40dd-be88-2a0b560fdfbfMathematicsORA Deposit2018Chang, JLyons, TNi, H<p>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. <em>inverting the signature of a path</em>.</p> <p>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.</p> |
| spellingShingle | Mathematics Chang, J Effective algorithms for inverting the signature of a path |
| title | Effective algorithms for inverting the signature of a path |
| title_full | Effective algorithms for inverting the signature of a path |
| title_fullStr | Effective algorithms for inverting the signature of a path |
| title_full_unstemmed | Effective algorithms for inverting the signature of a path |
| title_short | Effective algorithms for inverting the signature of a path |
| title_sort | effective algorithms for inverting the signature of a path |
| topic | Mathematics |
| work_keys_str_mv | AT changj effectivealgorithmsforinvertingthesignatureofapath |