Lecturer: Georg Lindgren
FormatThe plan is to meet approximately once a week for lectures and exercises, for example afternoon + following morning.
First meetingFriday, 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 coveredThe 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.
- How to define a stochastic process; sample space, ensemble, distribution
- Sample function properties, continuity, derivatives and integrals
- Covariance functions and their Fourier transform, spectral representation of the covariance function
- Spectral representation of a stationary process
- Linear filter operations, correlation- and spectral relations, white noise
- Hilbert transform, envelope, Karhunen-Loève expansion
- Classical ergodic theory, mixing conditions
- Multivariate processes and cross-correlation properties
- Spectral properties of random fields
- Level crossings and excursions, Rice's formula
Forthcoming introductory textbook on stationary processesA 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 processesWAFO, a MATLAB toolbox for Wave Analysis for Fatigue and Oceanography
Centre for Mathematical Sciences
Box 118, SE-221 00 Lund, Sweden
Phones & email addresses:+46 46 22 285 47 (office)
+46 46 22 285 50 (dept)
+46 46 22 246 23 (fax)
e-mail: georg (at) maths.lth.se