Graduate Course in Stochastic Processes Fall 99
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I will give a Graduate Course (doktorandkurs) in Stochastic Processes during september, 
october, and november. We will meet once or (most oftenly) twice a week (including some
exercise sessions), except for an occasional one-week break (during which we do not
meet at all). During weeks 36-41 (the upcoming six weeks) we have agreed to place our
meetings in the following time-slots (of which only one or two will be used each week)

   tuesday,  wednesday  and  friday  13.15-15.00  in room  S2.

The first meetings take place 

   friday 10 september in room G2 (not S2!)   and   wednesday 15 september (in room S2)
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The course is a "free" continuation of the course in Stable Processes that I gave 
during the spring semester. So it will be very awarding for people who followed the 
spring course to continue with the course this fall. But it is also quite possible and 
suitable for new participants [with a deacent probabilistic and/or mathematical back-
ground (as e.g., faculty members)] to join the course. If the need arises, I will 
prepare handouts listing things that one should know from the spring course. [Of course,
the full material (literature) that we used during the spring is also available.]  

The course will be quite entertaining, since stochastic processes are fun.

The course give five credits (fem poäng) for people who participate in the examination 
procedures (which consist of exercise sessions where the participants discuss exercises 
jointly with me). The exercises are not only intented to facilitate learning, but will 
sometimes also constitute important complements to material covered in the lectures.  

Examples of material that will be treated during the course are chapters 6, 7 and 9 in 
the book by Samorodnitsky and Taqqu. These chapters deal with 

   stable version of spectral-representation of second order (covariances) processes -
   stable processes with such a representation are called hamonizable (contrary to the 
   second order case there are a lot of non-harmonizable stable processes) - Chapter 6

   the important and time-lined concept of self-similarity (related to e.g., chaos and 
   fractals) in combination with the heavy tails and long-range dependence - Chapter 7

   issues related to the "high dimensionality" of a continuous time stochastic process
   (which of course are quite commonly used in applications and modelling), and how to 
   deal with and analyze such issues through finite or countably infinite methodology - 
   versions, notions of separability, measurability, continuity, etc. - Chapter 9

An example of further material I want to treat is 

   infinite divisibility - this is a very important generalization of stability which 
   turns out to contain VERY much (almost everything "sensible") - suprisingly, and 
   conveniently for us, many of the methods for stable processes have extensions to
   infinite divisibility - as the ability to treat infinitely divisible processes 
   improves and becomes "standardized", this class of processes will become more and
   more important in applications  as e.g., modelling (and not only in theory).

I will try to make it at least a little bit of a "general process course", and let 
stable and (to some extent) infinite divisible processes be the main body of processes
that the theory "operate on".

Please do not hesitate to contanct me (e.g., via email) if you have any question about 
the course. [We are just slightly on the low side in terms of number of participants 
(despite the well-known sucess of the course last spring), so I will be extremly keen 
to "accomodate" new (not already registered) participants.] 
 
Patrik Albin