Second order stochastic parabolic integro-differential equations driven by Wiener processes and Poisson martingale measures are considered. They arise in nonlinear filtering of partially observable jump-diffusions, and in many areas of physics and engineering. These equations may degenerate and can be PDEs with lower order (possibly fractional) differential operators.
The main result presented in the lectures is an existence, uniqueness and regularity theorem for the solutions of these equations. Its proof will use interpolation theorems from harmonic analysis and an It? formula obtained recently in a joint paper with Sizhou Wu for It?-Lévy type processes.
If time permits some numerical methods to approximate the solutions will also be discussed.
he main part of the lectures is based on joint papers with Marta de León-Contreras and Sizhou Wu.