CO905 Stochastic Processes
Online Course Materials 2008
Lecturer: Stefan Grosskinsky
A preliminary full version of the course notes: notes_co905.pdf
(updated on 06.02.2008 with few corrections)
Viva Timetable
The vivas will take place in Ellak Somfai's office PS103 on Monday, 11th February.
10:00  Tristan Webb  14:00  Andrew Wood  
10:30  Steven Hill  14:30  James Porter  
11:00  Marina Diakonova  15:00  Paul Chelboun  
11:30  Jamie Luo  
12:00  Jason Brentnall 
Changes in the timetable
 Monday, 4th Feb: Lectures from 9:00 to 11:00 and no classes
due to the MIR@W day DisCoMaths  Discrete Complex Systems and Probability
You are very welcome to attend!  Tuesday, 5th Feb: Classes from 3pm to 5pm instead of 1pm to 3pm
 Thursday, 7th Feb: Revision classes from 10 to 12 in seminar room B0.13 in mathematics
(PS017A is occupied)
Problem Sheets
 sheet1 (conditional probability, conditional expectation, discrete time Markov chains)
 sheet2 (continuoustime Markov chains, simulation of the Moran model)
CORRECTION: 20 marks for programming!
After a very useful discussion with Stephen more Remarks/CORRECTIONS:
 in Q2.1(a): a diagram is just a picture containing the three states connected their jump rates
 in Q2.4(c): measure the disctribution function of the NORMALIZED expected value (see sheet for details)
 in Q2.4(d): use alpha=1+1/N and 1+10/N instead of 2 and 5
 in Q2.4(e): use alpha=1 and 1+1/N instead of 1 and 2
 sheet3  part1 (Brownian motion and FokkerPlanck equations)
sheet3  part2 (Brownian motion and martingales)
CORRECTION: Definition of Brownian Bridge was wrong
Matlab and C stuff
 Matlab files for 1D, 2D and 3D Brownian motion: brownian.m, brownian2.m, brownian3.m
 C program moran.c and Matlab file moran.m for the Moran model
 Wikibooks on Matlab and C_Programming
 If you ever need a really good random number generator (not necessary for the module):
http://www.math.sci.hiroshimau.ac.jp/~mmat/MT/VERSIONS/CLANG/clang.html
http://en.wikipedia.org/wiki/Mersenne_Twister
Additional Literature
 R.A. Blythe, A.J. McKane: Stochastic Models of Evolution in Genetics, Ecology and Linguistics, J. Stat. Mech.: Theor. Exp. (2007) P07018

R. Lambiotte, S. Redner: Dynamics of NonConservative Voters, http://arxiv.org/abs/0712.0364

T. Antal, P. L. Krapvisky, S. Redner: Dynamics of Microtubule Instabilities, http://arxiv.org/abs/qbio/0703032

Joel L. Lebowitz: From Timesymmetric Microscopic Dynamics to Timeasymmetric Macroscopic Behavior: An Overview, http://arxiv.org/abs/0709.0724

Frank Kelly: The Mathematics of Traffic in Networks
 L.C.G. Rogers, D. Williams: Diffusions, Markov Processes and Martingales (Volume 1): Foundations, CUP (2000)
This is a (heavy!) Maths background for diffusion processes
Important Relevant Scientists
Andrey Markov, Robert Brown, Andrey Kolmogorov, Albert Einstein, Paul Langevin, Norbert Wiener, Paul Lévy, Max Planck, Adriaan Fokker, Kiyoshi Itō