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
• 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

 

Important Relevant Scientists

Andrey Markov, Robert Brown, Andrey Kolmogorov, Albert Einstein, Paul Langevin, Norbert Wiener, Paul Lévy, Max Planck, Adriaan Fokker, Kiyoshi Itō