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 Linear processes in function spaces (SS 2023)

Time and location
Seminar program
Last edited on
2023/05/18 by jj
Preliminary discussion:
Wednesday, April 19th, 2021, 11:15, MΛTHEMΛTIKON, INF 205, 4th floor, room 4.414

Please register for the seminar by using MÜSLI.

Time and location of the seminar:

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

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

Applied Mathematics, Stochastics

Description of the seminar:
Representation of continuous time stochastic processes as random variables in function spaces is an efficient tool in probability and statistics. The main purpose of this seminar is to study linear processes in Hilbert and Banach spaces, keeping in mind the above representation and applications to statistical prediction over a whole time interval. In this seminar we follow the book [1].

Possible presentation topics are:
Talks Subject
1/2 Stochastic processes and random variables in function spaces
3/4 Sequences of random variables in Banach spaces
5/6 Autoregressive Hilbertian Processes of Order 1
7/8 Estimation of Autocovariance Operators for ARH(1) Processes
9/10 Autoregressive Hilbertian Processes of Order p
11/12 Autoregressive Processes in Banach Spaces
13/14 General Linear Processes in Function Spaces
15/16 Estimation of Autocorrelation Operator and Prediction

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.

The seminar is for advanced Bachelor students and 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.

[1] D. Bosq: Linear processes in function spaces: theory and applications. (Lecture Notes in Statistics 149, Springer, New York, 2000) Link to PDF file

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