Research Seminar Stochastic: Prof Dr Günter Last "Chaos expansion and Malliavin calculus for the Dirichlet–Ferguson process"
Time : Tuesday , 4 pmOrganizer : Institute of Stochastics
Location :Ulm University, Helmholtzstraße 18, 220
As part of the research seminar organised by the Institute of Stochastics, Prof. Dr Günter Last, a professor at KIT – Karlsruhe Institute of Technology, will give a talk.
Title:"Chaos expansion and Malliavin calculus for the Dirichlet–Ferguson process"
| Date: Tuesday 19 May 2026 Venue: Room 220, Helmholtzstraße 18 Time: 4.00 pm |
Beforehand, from 3.30 pm in Room 200 (Helmholtzstraße 18), there will be an opportunity to meet for a coffee or tea.
Abstract:"The Dirichlet–Ferguson process ζ 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.
We shall present the fundamental chaos expansion by Peccati (2008), providing an explicit formula for the kernel functions.
We proceed to develop a Malliavin calculus for ζ. To this end, we introduce a gradient, divergence and a generator which act as linear operators on ζ-measurable
random variables or random fields and which are linked by some basic formulas such as integration by parts.
Whilst this calculus is motivated by Malliavin calculus for isonormal Gaussian processes and the general Poisson process, the strong dependence properties of ζ require
considerably more combinatorial effort. We will identify our generator as 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)."