Application of rough path theory for filtering and numerical integration methods

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In 1998 T. Lyons (Oxford) suggested a new approach for the robust pathwise solution of stochasticdifferential equations which is nowadays known as the rough path analysis. Based on thisapproach a new class of numerical algorithms for the solution of stochastic differential equationshave been developed. Recently, the rough path approach has been successfully extended also tostochastic partial differential equations. In stochastic filtering, the (unnormalized) conditionaldistribution of a Markovian signal observed with additive noise is called the optimal filter and itcan be described as the solution of a stochastic partial differential equation which is called theZakai equation. In the proposed project we want to apply the rough path analysis to a robustpathwise 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.