Graduate Course in Stochastic Simulation
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We have had a meeting today at 12.00 where we decided the times to be used 
for the course. Primarily, these times apply for the first part of the 
course, which will be given by me during the month of March. [There was
very few people at todays meeting, and although it is a bit unfair to the
people that really showed up, common (economical) sense says that we will
adapt the schedule to be able to house newcomers if that is necessary.] 

The times we agreed on are  Tuesday and Thursday  10.15-12.00  in room  S1.

First meeting is   TOMORROW THURSDAY 2 March.

NEXT WEEK there will be NO MEETINGS. However, I will distribute homework
(exercises) that you should work with that week. So the next meeting after
the one tomorrow is TUESDAY 14 MARCH.

My part of the course will use a part of the work "D. Knuth: The Art of
Computer Programming", and I will distribute xerox-copies of that part.
I will also use lecture-notes that I have prepared myself, which in part
points out the most important passages in Knuth, but also complements 
Knuth with additional "stochastic theory" (sepecially in the area of
simulation of stochastic processes).

Later parts of the course will be led by Holger Rootzen, and by Olle Hägg-
ström [who will talk about MCMC (Markov Chain Monte Carlo) as an "indepen-
dent" part of the continuation of his ongoing activity about complexity
(to my understanding).]

The topics to be treated by me (first part of course during March) are

1) Generation of random numbers with a uniform distribution over [0,1]
   in a computer - classical theory for congruence generators. Theses
   generators are the ones that are best understood at present, and also
   the only ones (I think) that are used in standard software. It is
   important to understand the performance and limitations of theses
   generators.

2) Generation of more general random variables in a computer - together
   with a lot of additional "connecting" material that are (necessary)
   standard knowledge within the field of simulation, as for example
   rejection sampling, importance sampling, multivariate random variables,
   methods for reducing variances (and thus number of replicas needed), ...

3) Testing of performance and limitations of random numbers generators:
   There are plenty of poor random number generators around (a famous
   example is an extremely poor generator used in IBM's 3070-mainframe
   computers during the seventies). Here we learn how to avoid the poorest
   ones - and also something about the difficult topic what "poor" really
   means.

4) Simulation of alpha-stable stochastic differential equations: These
   are equations of the type  dX(t) = a(t,X(t)) dt + b(t,X(t)) dW(t), and
   they are very important in applications, as for example mathematical
   finance. Here  X(t)  is a stocahstac process  (e.g., how some financial
   "parameter" varies with time), while  dW(t)  is a noise-process, which
   makes the equation stochastic (rather than deterministic). Traditionally
   the noise  W(t)  is a Wiener-processes. However, it is becoming increa-
   singly apparent that real-world applications (e.g., the wild fluctuations
   in finance) requires something quite different than a (Gaussian) Wiener
   process as noise. The natural first step towards a generalization (which
   conveniently also happens to be a major part of the whole stair) is to
   consider alpha-stable noise.  

Most people that have taken courses in mathematical statistice have heard
something about my four topics already. Now however, they are treated on the
level that is fit and proper for a graduate student. So although some of
the stuff relate to what you now already, the level will be higher than
previously.

In my opinion, good knowledge of simulation is as necessary as the most
basic graduate courses in probability and statistics nowadays, and it is 
really almost not possible to do reasearch without such knowledge. Also,
one should not believe that simulation "replaces theory" - rather these
to aspects of mathematical statistic complements and enriches each other,
and there are a lot of interesting, important and "timely" research going 
on here.

I will give 4-5 lectures, have about 3 exercise-sessions (which are part
of the grading-procedures), and finally two small programming-tasks where
one tests the methods in the computer (also part of the grading).

I will put copies of the copies of Knuths book outside the door to my
office (1424 - between Urban and Olle N) this afternoon (or evening).
My lecture-notes will be availbale via my personal www-page at latest
at the time when the corresponding lecture is delivered.

The language will be ENGLISH.

You are most wellcome.

Patrik Albin