AG Analysis & Stochastik

Prof. Dr. Anita Behme, Prof. Dr. Martin Keller-Ressel, Prof. Dr. Zoltán Sasvári,
Prof. Dr. René Schilling, Prof. Dr. Friedemann Schuricht, Prof. Dr. Ostap Okhrin

Winter 2024/25 - Winter term 2024/25

13.02.2025	Yuki Ueda (Hokkaido University of Education) "On the class of freely quasi-infinitely divisible distributions and an extension of Bercovici-Pata bijection"
28.11.2024 1:00 pm, Z21/381	Zbigniew Palmowski (Wrocław University of Science and Technology) "Stable random walks in cones" In this talk we consider a multidimensional random walk killed on leaving a right circular cone with a distribution of increments belonging to the normal domain of attraction of an $\alpha$-stable and rotationally-invariant law with $\alpha \in (0,2)\setminus \{1\}$. Based on Bogdan et al. (2018) describing the tail behaviour of the exit time of $\alpha$-stable process from a cone and using some properties of Martin kernel of the isotropic $\alpha$-stable process we construct a positive harmonic function of the discrete time random walk under consideration. Then we find the asymptotic tail of the distribution of the exit time of this random walk from the cone. We also prove the corresponding conditional functional limit theorem. This talk is based on the joint work with Wojciech Cygan, Denis Denisov, and Vitali Wachtel.
28.11.2024 2:00 pm, Z21/381	Krzysztof Bogdan (Wrocław University of Science and Technology) "Stable processes with reflections" We construct a Hunt process that can be described as the isotropic stable Lévy processes confined by reflections to a bounded open Lipschitz set. This is achieved through a direct analytic and potential-theoretic approach using the transition probability semigroup obtained in our earlier work, along with suitable excessive functions (barriers). Our method, based on nonlocal perturbations of integral kernels, offers a general alternative to the concatenation of Markov processes, previously applied in the literature and using complex probabilistic methods. We will also discuss applications to stationary distributions of the corresponding semigroup. This is a joint work with Markus Kunze (Universität Konstanz).
17.10.2024 1:00 pm, Z21/381	Callum Murphy-Barltrop (TU Dresden) "Modelling multivariate extremes with neural networks - is it possible to prove consistency?"

13.02.2025

Yuki Ueda (Hokkaido University of Education)

"On the class of freely quasi-infinitely divisible distributions and an extension of Bercovici-Pata bijection"

28.11.2024

1:00 pm, Z21/381

Zbigniew Palmowski (Wrocław University of Science and Technology)

"Stable random walks in cones"

In this talk we consider a multidimensional random walk killed on
leaving a right circular cone with a distribution of increments belonging to the normal domain of attraction of an $\alpha$-stable and rotationally-invariant law with $\alpha \in (0,2)\setminus \{1\}$.
Based on Bogdan et al. (2018) describing the tail behaviour of the exit time of $\alpha$-stable process from a cone and using some properties of Martin kernel of the isotropic $\alpha$-stable process
we construct a positive harmonic function of the discrete time random
walk under consideration.
Then we find the asymptotic tail of the distribution of the exit time of
this random walk from the cone.
We also prove the corresponding conditional functional limit theorem.
This talk is based on the joint work with Wojciech Cygan, Denis Denisov, and Vitali Wachtel.

28.11.2024

2:00 pm, Z21/381

Krzysztof Bogdan (Wrocław University of Science and Technology)

"Stable processes with reflections"

We construct a Hunt process that can be described as the isotropic
stable Lévy processes confined by reflections to a bounded open
Lipschitz set. This is achieved through a direct analytic and
potential-theoretic approach using the transition probability semigroup obtained in our earlier work, along with suitable excessive functions (barriers). Our method, based on nonlocal perturbations of integral kernels, offers a general alternative to the concatenation of Markov
processes, previously applied in the literature and using complex
probabilistic methods. We will also discuss applications to stationary
distributions of the corresponding semigroup. This is a joint work with
Markus Kunze (Universität Konstanz).

17.10.2024

1:00 pm, Z21/381

Callum Murphy-Barltrop (TU Dresden)

"Modelling multivariate extremes with neural networks - is it possible to prove consistency?"

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AG Analysis & Stochastik

Winter 2024/25 - Winter term 2024/25

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