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Graduate Course in Stochastic Processes, Third Quarter, Spring 2007



I will give a graduate course, 5 credits, with an option for participants to an individually enlarged course, Third quarter, January-March 2007, on selected topics from the field of (the vaste amount of material that can be brought under the umbrella of the label) "Stochastic Processes".

The focus will be on understanding, in a variety of ways, what Stochastic Processes are, and how they are dealt with technically. Problem solving and attention to technical skills will be a primary issue.

While working on understanding, problem solving and technical skills, we will encounter a variety of important classes of processes. The focus in the selection of this material will be on things a well-educated researcher in probability theory and stochastic processes really should know, in order to be able to communicate comfortably with international collegues, read journal articles etc.

Specifically, I will select material from the theory of Gaussian processes, stationary processes, continuous time Markov processes, together with self-similar processes and long-range dependence, and possibly including some extreme value theory. We will learn methods to study and describe these processes, that are of fundamental importance throughout the field of probability theory, including spectral and integral represetations, distribution theory, differences between weak and different strong representations, continuity properties, convergence concepts, etc.

However, if potential participants have views on what material to cover, I do welcome such proposals, and will consider them seriously!

As prerequisites for the course, students should have minimum one graduate course in probability theory. Obviously, familiarity with some type of stochastic processes from undegraduate or graduate studies, helps.

At the moment, I am not aware of any really well-suited single book for the planned activities, and I do suspect there there isn't one, although possibly "Kallenberg: Foundations of Modern Probability" could do a lot of the job. (The possible problem with this book is a considerable terseness.) However, I will check around for the best literature.

Best regards, and welcome, Patrik Albin
Email: palbin@math.chalmers.se
Telefon (Phone): +46 (31) 772 3512
Fax: +46 (31) 772 3508
Rum (Room): L 3072
Adress: Institutionen för Matematik, Avdelningen för Matematisk Statistik, SE-412 96 Göteborg, Sweden


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