Wednesday, July 22, 2026 - 16:30 in V3-201+Zoom
Differentiability of transition semigroup of generalized Ornstein-Uhlenbeck process: a probabilistic approach
A talk in the Bielefeld Stochastic Afternoon series by
Beniamin Goldys from University of Sydney
| Abstract: |
Let $X$ be a Banach space-valued Ornstein-Uhlenbeck process driven by a possibly degenerate Brownian Motion and let $P_t$ stand for its the transition operator. We provide a simple probabilistic proof of the fact that null-controllability of the corresponding deterministic system implies infinite Fr\'echet differ-entiability of $Pt\phi$ for every bounded Borel function $\phi$. We also provide a pointwise formula for all the derivatives of $P_t\phi$ in terms of multiple stochastic integrals. Applications to the analysis of transition semigroups in finite and infinite dimensions are given.
This is a joint work with Szymon Peszat
Within the CRC this talk is associated to the project(s): A5, B1 |
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