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Universität Augsburg
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Universität Augsburg
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Professor Ph.D. Fabio Bugini
Technische Universität Berlin
spricht am
Donnerstag, 21. November 2024
um
16:00 Uhr
im
Raum 2004 (L1)
über das Thema:
| Abstract: |
| This talk focuses on rough stochastic differential equations (rough SDEs) - introduced by Friz, Hocquet and Lê in 2021 - and to their relationship with rough partial differential equations (rough PDEs). Rough SDEs are driven simultaneously by a Brownian motion and a deterministic rough path, requiring both Itô's stochastic calculus and rough path theory for proper analysis. Their significance arises from applications in stochastic filtering with correlated noise, non-Markovian option pricing models, and particle systems with common noise. I will show that solving certain rough PDEs is essential in the aforementioned contexts. I will present results from [1] arXiv:2409.11330 (joint work with P. Friz and W. Stannat) and [2] arXiv:2402.12056 (joint work with M. Coghi and T. Nilssen). In [1], we develop a solution theory for linear rough PDEs, showing that solutions have a Feynman–-Kac type representation in terms of suitable rough SDEs. In [2], we apply Malliavin calculus to rough SDEs and extend Hörmander’s theory to the rough regime. |
| Hierzu ergeht herzliche Einladung. |
| Prof. Dr. Chengcheng Ling |