Prof. Dr. Peter Karl Friz
Prof. Dr. Wilhelm Stannat
Duration: 01.11.2011 - 31.10.2014
Technische Universität Berlin
In 1998 T. Lyons (Oxford) suggested a new approach for the robust pathwise solution of stochastic differential equations which is nowadays known as the rough path analysis. Based on this approach a new class of numerical algorithms for the solution of stochastic differential equations have been developed. Recently, the rough path approach has been successfully extended also to stochastic partial differential equations. In stochastic filtering, the (unnormalized) conditional distribution of a Markovian signal observed with additive noise is called the optimal filter and it can be described as the solution of a stochastic partial differential equation which is called the Zakai equation. In the proposed project we want to apply the rough path analysis to a robust pathwise solution of the Zakai equation in order to construct robust versions of the optimal filter. Subsequently, we want to apply known algorithms based on the rough path approach to the numerical approximation of these robust estimators and further investigate their properties.