Johannes Kepler Symposium für Mathematik

Im Rahmen des Johannes-Kepler-Symposiums für Mathematik wird Prof. Alfio Borzì, Institut für Mathematik, Universität Würzburg, am Thu, April 3, 2014 um 10:15 Uhr im S2 416-2 einen öffentlichen Vortrag (mit anschließender Diskussion) zum Thema "A Fokker-Planck Strategy to Control Stochastic Processes" halten, zu dem die Veranstalter des Symposiums,

O.Univ.-Prof. Dr. Ulrich Langer,
Univ.-Prof. Dr. Gerhard Larcher
A.Univ.-Prof. Dr. Jürgen Maaß, und
die ÖMG (Österreichische Mathematische Gesellschaft)

hiermit herzlich einladen.

Series B - Mathematical Colloquium:

The intention is to present new mathematical results for an audience interested in general mathematics.

A Fokker-Planck Strategy to Control Stochastic Processes

An efficient framework for the optimal control of probability density functions (PDF) of multidimensional stochastic processes and piecewise deterministic processes is presented. This framework is based on Fokker-Planck-type equations that govern the time evolution of the PDF of stochastic processes. In this approach, the control objectives may require to follow a given PDF trajectory or to minimize an expectation functional. Theoretical results concerning the forward and the optimal control problems are provided. In the case of stochastic (Ito) processes, the Fokker-Planck equation is of parabolic type and it is shown that under appropriate assumptions the open-loop bilinear control function is unique. In the case of piecewise deterministic processes (PDP), the Fokker-Planck equation consists of a first-order hyperbolic system. Discretization schemes are discussed that guarantee positivity and conservativeness of the forward solution. The proposed control framework is validated with multidimensional biological, quantum mechanical, and financial models. This work is supported by the EU Marie Curie International Training Network Multi-ITN STRIKE Projekt 'Novel Methods in Computational Finance' and in part by the ESF OPTPDE Programme.