Course Content

In this course we will study the continuous time nonlinear stochastic filtering problem and some of its applications to mathematical finance.

The program, time permitting, will be the following:

- Introduction of the problem

- The filtering problem as a measure valued random evolution.

- Review on stochastic processes and stochastic integration.

-The filtering equations: the Zakai and Kushner-Stratonovich equations.

- Properties of the solutions of the filtering equations.

- Finite dimensional filters: the Benes and Kalman-Bucy filter.

- Numerical methods: particle filters.

- Basics on discrete time stochastic filtering.  

- Applications to mathematical finance.

The main reference for the course is 

Bain, A. and Crisan, D. Fundamentals of Stochastic Filtering Springer Verlag 2009.

You have available this book in digital format through the UiO library.