Seminar Supervisor

Prof. Dr. Evgeny Spodarev

Seminar Advisor

Dr. Vitalii Makogin

Date and Place

It will be a two-day block-seminar.  The first day is January 13 (Friday) 9:00-17:00. The second day is January 20 (Friday) 8:00-15:00. Place: O28/2004 (13.01.2017), HeHo22/E03 (20.01.2017)

Prerequisites

The level of difficulty in this seminar is varying between the different topics. The audience is at least supposed to be familiar with basic probability. There are a few talks that require the lecture Stochastics II.

Intended Audience

Bachelor and Master Students of any mathematical study course.
The "(B)" in the list of talks, means that this talk is supposed to be given by a Bachelor's Student.

Content

Processes and fields with long-memory: Long-memory processes are known to play an important role in many scientific disciplines and applied fields such as geophysics, hydrology, economics, finance, telecommunications, network engineering, etc. In this course we investigate the connections between long-memory and other notions of interest, most importantly scaling and self-similarity. Self-similar processes such as fractional Brownian motion are stochastic processes that are invariant in distribution under suitable scaling of time and space. These processes can typically be used to model random phenomena with long-range dependence.The seminar starts with considering linear processes and self-similar processes. The next part is devoted to limit theorems in different frameworks. At the end we consider the generalization of long-range dependence to the case of higher dimensions.

(The picture shows the example of stochastic process with long range dependence)

Registration

To register for the seminar, please write an E-Mail to Vitalii Makogin until 15th October 2016. In the e-mail please give your name, matriculation number, your course of studies and subjects you have taken in the area of Probability or Statistics. 

Criteria to pass the seminar

Each student is supposed to give a talk, make slides and written presentation and to attend the seminar on a regular basis. Those who give a (good) talk and attend the seminar regularly will pass the seminar.

List of Talks

1. Spectral representation of stationary processes and sequences. (B) -- Qiannan Gao
2. Different types of memory. (B) -- Sebastian Korz
3. Linear processes. -- Vitalii Makogin
4. Hermite polynomials and Hermite expansion. (B) -- Mosleh Rostami
5. Multiple Wiener-Ito integrals and Hermite-Rosenblatt processes. 
6. Limit theorems for sums of processes with finite moments. -- Mariia Trotsko
7. Limit theorems for linear processes. -- Kirsten Schorning
8. Limit theorems for partial sums of stochastic volatility models. -- Stefan Roth
9. Limit theorems for sums of processes with infinite moments. -- Jürgen Kampf
10. Long memory random fields. -- Prof. Spodarev
11. Heuristic estimation of long memory. Density estimation. (B) -- Vitalii Makogin

Literature:

1. Beran, Jan, et al. "Long-memory processes: Probabilistic Properties and Statistical Methods." (2013).
2. Andersen, Torben Gustav, et al., eds. Handbook of financial time series. Springer Science & Business Media, (2009).
3. Lavancier, Frédéric. "Long memory random fields." Dependence in Probability and Statistics. Springer New York, 2006. 195-220.