Rasonyi, Miklos

Gyongy, Istvan

Sabanis, Sotirios

Dareiotis, Anastasios Constantinos

2016-01-29T15:13:20Z

2016-01-29T15:13:20Z

2015-11-26

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.

http://hdl.handle.net/1842/14186

en

The University of Edinburgh

K. Dareiotis. A Note On Degenerate Stochastic Integro-Differential Equations. arXiv:1406.5649.

K.Dareiotis and M. Gerencsér. AweakHarnack inequality for stochastic partial differential equations. arXiv:1503.04472.

K. Dareiotis and M. Gerencsér. On the boundedness of solutions of SPDEs. Stoch. Partial Differ. Equ. Anal. Comput., 3(1):84–102, 2015.

K. Dareiotis and I. Gyöngy. A Comparison Principle for Stochastic Integro- Differential Equations. Potential Analysis, 41(4):1203–1222, 2014.

K. Dareiotis and J.M. Leahy. Finite Difference Schemes for Linear Stochastic Integro-Differential Equations. arXiv:1310.4117.

stochastic partial differential equations

stochastic partial integro-differential equations

SPDEs

SPIDEs

Stochastic partial differential and integro-differential equations

Thesis or Dissertation

Doctoral

PhD Doctor of Philosophy