Signature inversion for monotone paths
The aim of this article is to provide a simple sampling procedure to reconstruct any monotone path from its signature. For every N, we sample a lattice path of N steps with weights given by the coefficient of the corresponding word in the signature. We show that these weights on lattice paths satisf...
| Hoofdauteurs: | , , , |
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| Formaat: | Journal article |
| Gepubliceerd in: |
University of Washington
2017
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| _version_ | 1826267733025619968 |
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| author | Chang, J Duffield, N Ni, H Xu, W |
| author_facet | Chang, J Duffield, N Ni, H Xu, W |
| author_sort | Chang, J |
| collection | OXFORD |
| description | The aim of this article is to provide a simple sampling procedure to reconstruct any monotone path from its signature. For every N, we sample a lattice path of N steps with weights given by the coefficient of the corresponding word in the signature. We show that these weights on lattice paths satisfy the large deviations principle. In particular, this implies that the probability of picking up a “wrong” path is exponentially small in N. The argument relies on a probabilistic interpretation of the signature for monotone paths. |
| first_indexed | 2024-03-06T20:58:43Z |
| format | Journal article |
| id | oxford-uuid:3a25275b-ee2f-424d-9918-a4035986bc8b |
| institution | University of Oxford |
| last_indexed | 2024-03-06T20:58:43Z |
| publishDate | 2017 |
| publisher | University of Washington |
| record_format | dspace |
| spelling | oxford-uuid:3a25275b-ee2f-424d-9918-a4035986bc8b2022-03-26T13:59:49ZSignature inversion for monotone pathsJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:3a25275b-ee2f-424d-9918-a4035986bc8bSymplectic Elements at OxfordUniversity of Washington2017Chang, JDuffield, NNi, HXu, WThe aim of this article is to provide a simple sampling procedure to reconstruct any monotone path from its signature. For every N, we sample a lattice path of N steps with weights given by the coefficient of the corresponding word in the signature. We show that these weights on lattice paths satisfy the large deviations principle. In particular, this implies that the probability of picking up a “wrong” path is exponentially small in N. The argument relies on a probabilistic interpretation of the signature for monotone paths. |
| spellingShingle | Chang, J Duffield, N Ni, H Xu, W Signature inversion for monotone paths |
| title | Signature inversion for monotone paths |
| title_full | Signature inversion for monotone paths |
| title_fullStr | Signature inversion for monotone paths |
| title_full_unstemmed | Signature inversion for monotone paths |
| title_short | Signature inversion for monotone paths |
| title_sort | signature inversion for monotone paths |
| work_keys_str_mv | AT changj signatureinversionformonotonepaths AT duffieldn signatureinversionformonotonepaths AT nih signatureinversionformonotonepaths AT xuw signatureinversionformonotonepaths |