MVE170/MSG800 Basic Stochastic Processes Course Mail 3

Skickat: den 27 november 2013 15:17

Hello!

During the lecture today Thursday 27 November I cited the convergence theorem 
for continuous time Markov chains (Theorem 6.9.21 in G&G) a bit erroneously - 
the correct version of the results reads that if an irreducible continuous 
time Markov chain has a stationary distribution pi, then p_{ij}(t) -> pi_j as 
t->oo, while if the chain does not have a stationary distribution, then 
p_{ij}(t) -> 0 as t-> oo.

During the remaining 8 teaching sessions we have scheduled for the course (5 
lecture sessions and 3 exercise sessions) I will not necessarily strictly obey  
the scheme indicated in the course programme (and elsewere) about what time 
should be lecture time and what time should be exercise time, but instead 
allow myself to rearrange a little between the two to obtain the most logical 
order between lectures and the corresponding exercises. Specifically - 
tomorrow Thursday 28 November I expect to finish doing exercises before the 
exercise session 8-10 have ended and will then use the latter part of that 
exercise session for lecturing. On the other hand, next week on Thursday 5 
December I expect the exercise session 8-10 to intrude on the lecture time 
10-12, so I will start to lecture first when I am done with the exercises. 
Finally, on the lecture time the last Thursday 12 December 10-12 I hope to 
have finished lecturing the whole course already before that so I will then 
instead use that lecture session for doing exercises.

Note that our last course topic Queueing Theory (checkout that word with 5 
straight wouls by the way!) - Chapter 9 in Hsu - that this topic is in fact 
more or less a special case of Section 6.11 (birth and death processes) in 
G&S. Thus we have more or less done Queues already by means of Section 6.11 
in G&S (which we started to talk about today) and need only sort of 
familiarize ourselves with the language when we come to Chapter 9 in Hsu :) 
... .

On the written exam querys will be more or less evenly spread over the stuff 
we have talked about during lectures and exercised ourselves with in 
exercises. Specifically - long and complicated proofs in G&S (for example (or 
mainly even), the proofs of the convergence theorems in Section 6.4), which 
we have not talked about during lectures, they are not included as mandatory 
reading, and frankly I advice to skip them. As we spend much time on the 
material in the G&S book we must obviously have at least one exam query that 
relates to that material. But as this material has not featured in the course 
previously I will restrict the number of queries that require the more 
complete Markov theory in G&S (that is, the less ambitious theory in Hsu is 
not good enough ...) - I will restrict that number of querys to exactly one 
(=1). As for computational problems, there will also be exactly one such, in 
the fashion of the computational problems of the exercise sessions. And then 
I try to find a problem on Gauss, one on martingale, etc until course 
material is evenly covered, where one of these querys as mentioned already is 
computational.

You must register for the written exam to be guaranteed a seat at it 
(although virtually always they will be able to accomodate you anyway). If 
you do not know how to register for a exam, please ask a fellow student.
The written exam is Monday 16 December 2-6 pm in house V - again ask a fellow 
student where that is if you do not know already. I will visit the written 
exam 3 pm and 5 pm to answer questions about it. I do in general not mind at 
all to explain what I mean in exam questions so you need not really worry 
about missing some little detail of terminology - if you are not sure what I 
mean on the written exam because of the language you can generally ask about 
it.

I usually (if nothing unforseen happens) grade the written exam A S A P - 
meaning at latest the day after the exam was held. Then I send you the result 
by email in coded form - I simply tell what was the exam result for each 
secret exam code - you must therefore remember your personal secret exam code 
in order to be able to find your result. Otherwise I cannot help you with it 
- remember that grading is anonymous. It can then take quite a bit of time - 
this varies widely - sometimes it goes quick and sometimes it takes very long 
time - anyway, regardless of how much time it takes, you will eventually 
recive an official result email with your exam result (same as what I sent 
you right after exam unless there has been some processing error somewhere). 
THEN (but not earlier) you can go to our expedition and take a look at the 
grading of your exam, should you wish to do that. You can also file a written 
complaint on elements of the grading, should you wish to do that, which I 
will then recive and take a renewed look at. As our expedition closes for 
x-mas holidays after the exam week it might happen that it is first after 
Ephiphany (trettonhelgen) when the expedition reopens that you can do the 
above mentioned.

Reexams, should you need them, are in Eastern period and after summer period, 
see the course programme.

I kraft av mitt ämbete
Patrik Albin, examinator Basic Stochastic Processes