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).
