Tuesday, July 11, 2023 - 11:00 in ZiF
On rough stochastic differential equations
A talk in the SPDEs, optimal control and mean field games series by
Peter K. Friz from Berlin
| Abstract: |
I will survey the key ideas of [Rough stochastic differential equations, F-Hocquet-Lê,
arXiv2106.10340], a hybrid theory that combines Itô's stochastic - and Lyons'
rough differential equations. A major role is played by a new stochastic variant
of Gubinelli's controlled rough paths spaces, with norms related to Lê's stochastic
sewing lemma. Applications included filtering, pathwise stochastic control,
the analysis of interacting particle systems with common noise and related classes
stochastic partial differential equation. Time permitting, I will present recent
discrete approximation results (joint work with Lê-Zhang), and an application
to mathematical finance (joint wort with C. Bayer, P. Bank, L. Pelizzari).
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