Ansicht nach Raum E-N 189

This lecture is devoted to some fundamental recent progress in stochastic

analysis, a hybrid theory which seamlessly combines the advantages of both

Itô's stochastic - and Lyons' rough path theory. We rely in particular on a

new stochastic variant of controlled rough paths spaces, inspired by Khoa

Lê's celebrated stochastic sewing lemma. There are many applications,

included robust filtering, pathwise stochastic control, conditional

analysis of financial models, and the analysis of mean field SDEs with

common noise, as well as related classes of non-linear stochastic partial

differential equation. Time and audience permitting we shall discuss this

in later parts of the lecture.

Prerequisites: measure theory, awareness of Itô's stochastic differential

equations, as taught in FiMa2 (TU), WT3 (TU), or Stochastic Processes II

(BMS)

Time + location: information available on

https://page.math.tu-berlin.de/~friz/ (Link Student Info)

References:

  -

  Le Gall, Jean-François. Brownian motion, martingales, and stochastic

  calculus. springer publication, 2016.

  -

  Friz, Peter K., and Martin Hairer. A course on rough paths. Springer

  International Publishing, 2020.

  -

  Friz, Peter K., Antoine Hocquet, and Khoa Lê. "Rough stochastic

  differential equations." arXiv preprint arXiv:2106.10340 (2021).