CO905 Stochastic Processes

Online Course Materials 2008

A preliminary full version of the course notes: notes_co905.pdf
(updated on 06.02.2008 with few corrections)

The vivas will take place in Ellak Somfai's office PS103 on Monday, 11th February.

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)

sheet1 (conditional probability, conditional expectation, discrete time Markov chains)
sheet2 (continuous-time 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
These changes can be found in the online version of the sheet above.
sheet3 - part1 (Brownian motion and Fokker-Planck equations)
sheet3 - part2 (Brownian motion and martingales)
CORRECTION: Definition of Brownian Bridge was wrong

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.hiroshima-u.ac.jp/~m-mat/MT/VERSIONS/C-LANG/c-lang.html
http://en.wikipedia.org/wiki/Mersenne_Twister

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 Non-Conservative Voters, http://arxiv.org/abs/0712.0364
T. Antal, P. L. Krapvisky, S. Redner: Dynamics of Microtubule Instabilities, http://arxiv.org/abs/q-bio/0703032
Joel L. Lebowitz: From Time-symmetric Microscopic Dynamics to Time-asymmetric 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