Seminar - Stochastic flows with interaction and random measures

WS 2020/21


Seminar talks: Friday 10:15 - 11:45, Online, link to Zoom

Office hours: Thursday 16:00 - 17:30, Online, link to Zoom (different from course link)


Course in the Moodle system: link


Talks can be given in English or German



SHORT DESCRIPTION OF SEMINAR


Stochastic flows arise naturally in statistical physics, biology, hydrodynamics, etc. and are usually used for the description of dynamics of infinitely many interacting particles moving in random media. The aim of the seminar is to discuss some important results obtained for flows generated by stochastic differential equations. We will be interested in the case where the motion of particles is not only determined by a stochastic differential equation but also depends on the mass that particles transfer. This will lead us to some unification of the theory of stochastic flows and measure-valued processes. In particular, we will discuss the following topics


  • stochastic flows generated by stochastic differential equations;
  • Brownian sheet and related stochastic calculus;
  • random measures;
  • stochastic differential equations with interactions;
  • evolutionary measure-valued processes;
  • integrals with respect to random measures and equations driven by a random measure;
  • weak compactness and stationary measure-valued processes.


    • REQUIRED KNOWLEDGE


    The seminar requires knowledge of standard courses on stochastic processes. However, we also kindly invite students who have taken only the probability theory course. Since the topic of the seminar is quite wide, we will try to propose topics for the presentation that will correspond to the level of speakers. The list of topics will be offered approximately one week after the end of the registration.



    LIST OF TOPICS


    The list



    SOME LITERATURE


  • A. Dorogovtsev and P. Kotelenez "Stochastic flows with interaction and random measures" in preparation
  • A. Etheridge "An introduction to superprocesses"
  • S. Ethier and T. Kurtz "Markov processes: Characterization and convergence"
  • D. Dawson "Measure-valued Markov processes"
  • H. Kunita "Stochastic flows and stochastic differential equations"
  • O. Kallenberg "Foundations of modern probability"
  • N. Ikeda and S. Watanabe "Stochastic differential equations and diffusion processes"