Kusuoka–Stroock gradient bounds for the solution of the filtering equation
We obtain sharp gradient bounds for perturbed diffusion semigroups. In contrast with existing results, the perturbation is here random and the bounds obtained are pathwise. Our approach builds on the classical work of Kusuoka and Stroock [13], [14], [16], [17], and extends their program developed fo...
| Main Authors: | , , |
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| Format: | Journal article |
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Elsevier
2015
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| _version_ | 1797103053377110016 |
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| author | Crisan, D Litterer, C Lyons, T |
| author_facet | Crisan, D Litterer, C Lyons, T |
| author_sort | Crisan, D |
| collection | OXFORD |
| description | We obtain sharp gradient bounds for perturbed diffusion semigroups. In contrast with existing results, the perturbation is here random and the bounds obtained are pathwise. Our approach builds on the classical work of Kusuoka and Stroock [13], [14], [16], [17], and extends their program developed for the heat semi-group to solutions of stochastic partial differential equations. The work is motivated by and applied to nonlinear filtering. The analysis allows us to derive pathwise gradient bounds for the un-normalised conditional distribution of a partially observed signal. It uses a pathwise representation of the perturbed semigroup following Ocone [22]. The estimates we derive have sharp small time asymptotics. |
| first_indexed | 2024-03-07T06:14:35Z |
| format | Journal article |
| id | oxford-uuid:f0a59d22-96ec-49df-84da-8b96d61286cf |
| institution | University of Oxford |
| last_indexed | 2024-03-07T06:14:35Z |
| publishDate | 2015 |
| publisher | Elsevier |
| record_format | dspace |
| spelling | oxford-uuid:f0a59d22-96ec-49df-84da-8b96d61286cf2022-03-27T11:49:44ZKusuoka–Stroock gradient bounds for the solution of the filtering equationJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:f0a59d22-96ec-49df-84da-8b96d61286cfSymplectic Elements at OxfordElsevier2015Crisan, DLitterer, CLyons, TWe obtain sharp gradient bounds for perturbed diffusion semigroups. In contrast with existing results, the perturbation is here random and the bounds obtained are pathwise. Our approach builds on the classical work of Kusuoka and Stroock [13], [14], [16], [17], and extends their program developed for the heat semi-group to solutions of stochastic partial differential equations. The work is motivated by and applied to nonlinear filtering. The analysis allows us to derive pathwise gradient bounds for the un-normalised conditional distribution of a partially observed signal. It uses a pathwise representation of the perturbed semigroup following Ocone [22]. The estimates we derive have sharp small time asymptotics. |
| spellingShingle | Crisan, D Litterer, C Lyons, T Kusuoka–Stroock gradient bounds for the solution of the filtering equation |
| title | Kusuoka–Stroock gradient bounds for the solution of the filtering equation |
| title_full | Kusuoka–Stroock gradient bounds for the solution of the filtering equation |
| title_fullStr | Kusuoka–Stroock gradient bounds for the solution of the filtering equation |
| title_full_unstemmed | Kusuoka–Stroock gradient bounds for the solution of the filtering equation |
| title_short | Kusuoka–Stroock gradient bounds for the solution of the filtering equation |
| title_sort | kusuoka stroock gradient bounds for the solution of the filtering equation |
| work_keys_str_mv | AT crisand kusuokastroockgradientboundsforthesolutionofthefilteringequation AT littererc kusuokastroockgradientboundsforthesolutionofthefilteringequation AT lyonst kusuokastroockgradientboundsforthesolutionofthefilteringequation |