In this work we present some new results concerning stochastic partial differential and integro-differential equations (SPDEs and SPIDEs) that appear in non-linear filtering. We prove existence and uniqueness of solutions of SPIDEs, we give a comparison principle and we suggest an approximation scheme for the non-local integral operators. Regarding SPDEs, we use techniques motivated by the work of De Giorgi, Nash, and Moser, in order to derive global and local supremum estimates, and a weak Harnack inequality.
| Identifer | oai:union.ndltd.org:bl.uk/oai:ethos.bl.uk:679456 |
| Date | January 2015 |
| Creators | Dareiotis, Anastasios Constantinos |
| Contributors | Rasonyi, Miklos ; Gyongy, Istvan ; Sabanis, Sotirios |
| Publisher | University of Edinburgh |
| Source Sets | Ethos UK |
| Detected Language | English |
| Type | Electronic Thesis or Dissertation |
| Source | http://hdl.handle.net/1842/14186 |
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