Johannes Kepler Symposium on Mathematics

As part of the Johannes Kepler symposium on mathematics Prof. Alfio Borzì, Institut für Mathematik, Universität Würzburg, will give a public talk (followed by a discussion) on Thu, April 3, 2014 at 08:15 o'clock at S2 416-2 on the topic of "A Fokker-Planck Strategy to Control Stochastic Processes" . The organziers of the symposium,

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

hereby cordially invite you.

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.