Graduate Course in Stochastic Processes Fall 99
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Provided that there is sufficient interest, 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 a couple of one-week breaks (during which we
do not meet at all). There will be an 

   INTRODUCTORY MEETING in room S2 Friday 3 September 12.30-13.00.

During the introductory meeting we will agree on suitable times for our
lectures and exercises. Please try to contact me before noon friday (e.g., 
via email) if you cannot attend this meeting. People who intend to just 
"sit in" on the lectures, but do not feel that they are "serious enough" 
participants to come to the introductory meeting (and affect the scheduling) 
could also indicate their interest by an email (so that I know about you).

The course is a "free" continuation of the course in Stable Processes that 
I gave during the spring semester (mid april through mid june). This means
that 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 background) to 
join the course. I will prepare some handouts that list things that one 
should know from the spring course.

The course will give five credits (fem poäng) for people who participate 
(and pass) the examination procedures, which consists of several 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 

     the alpha-stable version of the spectral-representation of a second
     order (i.e., with covariances) process; alpha-stable processes that
     possess such a representation are called hamonizable - [however (con-
     trary to the second order case) there exist a lot of alpha-stable
     processes that are not hamonizable] - Chapter 6

     the vastly important and "current" concept of self-similarity 
     (closely related to chaos and fractals); here in combination with 
     the equally timelined concept of heavy tails -  Chapter 7

     the fundamental problem with the infinite-dimensionality of a
     stochastic process, and how to deal and analyze this through
     finite-dimensional methodology - this involves important concepts
     as  versions, (various notions of) separability, measuarability,
     continuity, boundedness etc.  of paths of the process - Chapter 9

Examples of further material likely to treated are 

     "general theory" and "foundations of the theory" of stochastic processes
     - here we e.g., learn how to use differnt concepts of separability to 
     draw conclusions about a whole (uncountable) process from countable data,
     and also to see the difference between different concepts of equality or
     convergence when applied to (uncountably) infinite-dimensional objects
     like processes (often are)

     infinite divisible processes - this is a very important generalization
     of stability which turns out to contain very VERY much (in fact, almost
     everything) - suprisingly, and conveniently for us, many of the methods
     we have learned for stable processes carry over to this general objects

I will try to make the course a least a bit of a "general process course", 
and then use stable and, to some extent, infinite divisible processes as the
main body of processes to let the theory "work on".

Please do not hesitate to contanct me (e.g., via email) if you have any
question about the course.
 
Patrik Albin