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Universität Augsburg
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Universität Augsburg
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Professor Dr. Günter Last
KIT
spricht am
Mittwoch, 3. Juni 2026
um
10:30 Uhr
im
Raum 2004 (L1)
über das Thema:
| Abstract: |
| The Dirichlet--Ferguson process $\zeta$ is a random, purely discrete, probability measure, whose finite-dimensional distributions are Dirichlet distributions. It can be defined on a general state space and has numerous applications, such as in population genetics or Bayesian statistics. We shall start the talk with presenting the fundamental chaos expansion from Peccati (2008). We can provide an explicit formula for the kernel functions. Then we proceed with developing a Malliavin calculus for $\zeta$. We introduce a gradient, divergence and a generator which act as linear operators on $\zeta$-measurable random variables or random fields and which are linked by some basic formulas such as integration by parts. While this calculus is motivated by Malliavin calculus for isonormal Gaussian processes and the general Poisson process, the strong dependence properties of $\zeta$ require considerably more combinatorial efforts. We will show that our Malliavin generator is in fact the generator of the Fleming--Viot process and describe the associated Dirichlet form explicitly in terms of the chaos expansion. If time permits, we shall also present a short direct proof of the Poincaré inequality. The talk is based on joint work with Babette Picker (Karlsruhe). |
| Hierzu ergeht herzliche Einladung. |
| Prof. Dr. Markus Heydenreich |