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PhD-course in Stationary stochastic processes

The course is intended for PhD-students in mathematical statistics, mathematics, signal processing, automatic control and other fields. It will be based on the new book Stationary stochastic processes: Theory and applications that appeared in October 2012 at Chapman & Hall/CRC.

Lecturer: Georg Lindgren

Format

The plan is to meet approximately once a week for lectures and exercises, for example afternoon + following morning.

First meeting

Friday, February 22, at 10.30 in Mh 227. We will then plan for a schedule that suits best. If you can not attend, please send me a note with your "cannot's" and preferences.

Topics to be covered

The main idea in the course is to present how stationary process models are constructed and how their mathematical, probabilistic, and statistical properties can be analysed. It is intended as a "second course" in stationary processes; some previous knowledge from mathematical statistics or signal processing helps. Here is a list of what is cover. Note: Part I, 1-6, gives 7.5 ECTS, Part I+II, 1-10, gives 10 ECTS.

1. How to define a stochastic process; sample space, ensemble, distribution
2. Sample function properties, continuity, derivatives and integrals
3. Covariance functions and their Fourier transform, spectral representation of the covariance function
4. Spectral representation of a stationary process
5. Linear filter operations, correlation- and spectral relations, white noise
6. Hilbert transform, envelope, Karhunen-Loève expansion
7. Classical ergodic theory, mixing conditions
8. Multivariate processes and cross-correlation properties
9. Spectral properties of random fields
10. Level crossings and excursions, Rice's formula

Forthcoming introductory textbook on stationary processes

A new textbook Stationary stochastic processes for scientists and engineers is planned to appear in July/August 2013 at Chapman & Hall/CRC, by myself, Holger Rootzén and Maria Sandsten.

Useful Matlab package for experiments with stationary processes

WAFO, a MATLAB toolbox for Wave Analysis for Fatigue and Oceanography