Univ. Heidelberg
Statistics Group   Institute for Mathematics   Faculty of Mathematics and Computer Science   University Heidelberg
Ruprecht-Karls-Universität Heidelberg Statistics of inverse problems Research Group Seminar Statistics for discretely observed Lévy processes (WS 2023/24)
english


Time and location
Seminar program
Requirements
References Last edited on
2023/10/12 by jj.
Preliminary discussion:
Wednesday, October 18th, 2023, 12:00, MΛTHEMΛTIKON, INF 205, 4th floor, room 4.414

Registration:
Please register for the seminar by using MÜSLI.

Time and location of the seminar:
The seminar will be held as a Blockseminar on two days in January 2024.

Contact:
Maximilian Siebel <siebel[at]math.uni-heidelberg.de>
Bianca Neubert <neubert[at]math.uni-heidelberg.de>
Prof. Dr. Jan JOHANNES <johannes[at]math.uni-heidelberg.de>
Questions, please directly by email or by using the contact form.

Language:
The seminar will be in English, if there is at least one non-German speaking participant.

Field:
Applied Mathematics, Stochastics

Description of the seminar:
In probability theory, a Lévy process is a stochastic process with independent, stationary increments: it represents the motion of a point whose successive displacements are random, in which displacements in pairwise disjoint time intervals are independent, and displacements in different time intervals of the same length have identical probability distributions. The most well known examples of Lévy process are the Brownian motion and the Poisson process. In this seminar we want to introduce Lévy processes in a mathematically rigorous way and study statistical techniques whenever discrete observations of Lévy processes are available.

Possible presentation topics are:

Talks Subject Source
1. Lévy processes and applications (K) 1 & 2.1
2. Properties of Lévy processes (K) Selected topics of 2 & 3
3. Spectral estimation of the Lévy triplet (LM) Belomestny & Reiß: 1 - 4
4. Rate Optimality for the triplet estimation (LM) Belomestny & Reiß: 5
5. Estimation of a Lévy density (LM) Comte & Genon-Catalot 1-4.1.2
6. Adaptive Estimation of a Lévy density (LM) Comte & Genon-Catalot 4.1.3
7. Estimation of a Lévy density on a compact set (LM) Comte & Genon-Catalot 4.2
8. Estimation of a Lévy density - kernel estimators (LM) Comte & Genon-Catalot 4.3
9. Estimation of Gaussian and non-Gaussian components (LM) Comte & Genon-Catalot 5-7
10./11. Parametric estimation of Lévy processes: MLE approach (LM) Masuda 1-2
12./13. Parametric estimation of stable Lévy processes (LM) Masuda 3
14./15. Uniform tail-probability estimate of statistical random fields (LM) Masuda 4
Each participant is expected to give a 60 minutes. A handout containing the most important definitions and results as well as short sketches of the proofs should be prepared for the other participants.

Requirements:
The seminar is for advanced Master students who want to specialize in statistics and are already familiar with the topics typically covered in the lectures Probability Theory I and II and Statistics I and II.

Reference:
(K) Kyprianou: Fluctuations of Lévy Processes with Applications
(LM) Belomestny, Comte, Genon-Catalot, Masuda & Reiß: Lévy Matters IV: Estimation for Discretely Observed Lévy Processes
Contact
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