Stationary Stochastic Processes Lectures

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This is a repo for a couple of lectures on stationary stochastic processes that I have given at Stockholm University.

Contents

• Intro to stationary stochastic processes
• Correlation properties
• Spectral properties
• Periodogram and inference
• Mean square convergence
• Spectral representation of stationary stochastic processes

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Course literature and Schedule

The lectures will be based on parts of the following books:

• Lindgren, G. Rootzén, H. and Sandsten, M. (2014). Stationary Stochastic Processes for Scientist and Engineers, CRC Press. (abbreviated LRS)
• Lindgren, G. (2014). Stationary Stochastic Processes, CRC Press. (abbreviated LAdv)

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Teacher

Mattias Villani, Lecturer
Professor, Natural Born Bayesian 😜
Department of Statistics, Stockholm University

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Lecture 1 - Stationary stochastic processes and spectral properties
Reading: LRS Ch. 1, 2.1-2.3, 2.4.1-2.4.2, 2.5.1-2.5.2, 2.5.4, 4.1-4.4 | Slides
Extra: trig cheat sheet | Appendix A on complex exponentials

Lecture 2 - Spectral properties, inference and linear filters
Reading: LRS Ch. 5.1—5.3.1, 6.1-6.3 | LAdv Ch. 2.1.1-2.1.2, 3.3.1-3.3.2, 3.3.7 | Slides