CO905 Stochastic Processes
Online Course Materials
Lecturer: Stefan Grosskinsky
A preliminary version of the full course notes: notes_co905_09.pdf
Lectures: Mon 10-12 and Tue 10-12 in D1.07
Classes: Mon 2-4 and Thu 10-12 in D1.07
Vivas: Fri 6th Feb
Current Viva Timetable
The vivas will take place in the workroom D1.13 on Friday 6th February.
Remember that the first 4 minutes you should say something about a talk of your choice fromo the MIR@W day.
9:40 | Jon Mascie-Taylor | 11:20 | Dan Barker | |
14:00 | Oliver Hambrey | |
10:00 | Jamie Harris | 11:40 | Anthony Woolcock | 14:20 | Jennifer Dudley | ||
10:20 | Martine Barons | 12:00 | Sam Brand | 14:40 | Ali Adnan | ||
10:40 | Viki Sgardeli | 12:20 | Daniel Peavoy | 15:00 | Quentin Caudron |
Changes in the timetable
- Mon 2nd Feb and Tue 3rd Feb: MIR@W Day Aggregation, condensation and coagulation in particle systems
Mon: Lectures from 10-12 consist of an introduction to the topic, no classes (instead go to some of the talks)
Tue: No lectures (instead go to some of the talks)
Problem Sheets
- sheet1: conditional probability, Markov processes, branching processes (due on 13.01.)
- sheet2: continuous time Markov chains, birth-death processes, maximum entropy (due on 22.01.)
Q2.4: please add a minus sign in the definition of the entropy (changed in online version) - sheet3: Brownian motion, continuity equation, simulation of a traffic model (due on 30.01.)
Q3.2(b): please replace the 'x's in the conservation law by 'y's (changed in online version)
Matlab and C stuff
- Very simple C program traffic.c and Matlab file traffic.m for a basic traffic model
- Matlab files for 1D, 2D and 3D Brownian motion: brownian.m, brownian2.m, brownian3.m
Einsteins explanation of Brownian motion: http://galileoandeinstein.physics.virginia.edu/more_stuff/Applets/brownian/brownian.html - 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
Additional Literature
- R.A. Blythe, A.J. McKane: Stochastic Models of Evolution in Genetics, Ecology and Linguistics, J. Stat. Mech.: Theor. Exp. (2007) P07018
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R. Lambiotte, S. Redner: Dynamics of Non-Conservative Voters, http://arxiv.org/abs/0712.0364
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T. Antal, P. L. Krapvisky, S. Redner: Dynamics of Microtubule Instabilities, http://arxiv.org/abs/q-bio/0703032
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Joel L. Lebowitz: From Time-symmetric Microscopic Dynamics to Time-asymmetric Macroscopic Behavior: An Overview, http://arxiv.org/abs/0709.0724
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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