Stochastic partial differential and integro-differential equations
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Date
26/11/2015Author
Dareiotis, Anastasios Constantinos
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Abstract
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.