Prof. Dr. Peter Karl Friz

Projects as a project leader

  • C-SE8

    Stochastic methods for the analysis of lithium-ion batteries

    Prof. Dr. Wolfgang Dreyer / Prof. Dr. Peter Karl Friz

    Project heads: Prof. Dr. Wolfgang Dreyer / Prof. Dr. Peter Karl Friz
    Project members: Paul Gajewski / Dr Mario Maurelli
    Duration: 01.06.2014 - 31.05.2017
    Status: running
    Located at: Weierstraß-Institut


    The aim of the project is to better understand and to give simulations for a successful model for the charging and discharging of lithium-ion batteries, which are currently the most promising storage devices to store and convert chemical energy into electrical energy and vice versa. The model exhibits phase transition under different small parameter regimes and gives rise to hysteresis. We study these phenomena using the interpretation of the model as a stochastic particle system, with the goal of providing stability bounds, fast simulations, improvement of the model itself and optimization of the device. More information...
  • D-AP27

    Application of rough path theory for filtering and numerical integration methods

    Prof. Dr. Peter Karl Friz / Prof. Dr. Wilhelm Stannat

    Project heads: Prof. Dr. Peter Karl Friz / Prof. Dr. Wilhelm Stannat
    Project members: -
    Duration: 01.11.2011 - 31.10.2014
    Status: completed
    Located at: Technische Universität Berlin


    In 1998 T. Lyons (Oxford) suggested a new approach for the robust pathwise solution of stochastic di fferential 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 di fferential equations. In stochastic filtering, the (unnormalized) conditional distribution of a Markovian signal observed with additive noise is called the optimal fi lter and it can be described as the solution of a stochastic partial diff erential 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.