CO905 Stochastic Processes

Online Course Materials

Lecturer: Stefan Grosskinsky

Final version of the course notes: notes_co905_10.pdf

Lectures: Thu 10-12 and Fri 10-12 in D1.07

Classes: Tue 14-16 and Fri 14-16 in D1.07

Vivas: Thu 11th Feb

Viva timetable

The vivas will take place in the workroom D1.13 on Thursday 11th February.
Remember that the first 3 minutes you should say something about a subject of your choice related to the module or the MIR@W day.

11:00	Chris Oates		15:10	Yu-Xi Chau
11:20	Sergio Morales-Enciso		15:30	Leigh Robinson
11:40	Nicolai Peremezhney		15:50	Pantelis Hadjipantelis
12:00	Matthew Graham		16:10	Alistair Tucker
12:20	Anas Rana		16:30	Rebecca Langham

Changes/Related Events

• Thu 11th Feb and Fri 12th Feb no lectures due to vivas
• Tue 9th Feb: Revision class (2-4pm)
  
• Mon 8th Feb: MIR@W day Burgers equation and applications
  This event is officially part of the module and you are expected to attend...
  
• Mon 11th Jan to Wed 13th Jan:
  Symposium workshop Non-equilibrium dynamics of spatially extended interacting particle systems
  This workshop is particularly suitable for CO905. You are encouraged to attend, please have a look at the abstracts. Most accessible should be talks on Tuesday and Wednesday.
  
• There will be no class on Tue 12th Jan due to the workshop and on Fri 15th Jan due to the open day, lectures from 10-12 run as usual that week.
  

Worksheets/Assessments

• sheet1: Markov processes, random walks, branching processes (due 20.01., 25/100 marks)
• sheet 2: continuous time Markov chains, birth-death processes, simulation of contact process (due 29.01., 25/100 marks)
  
• sheet 3: Contact process (mean-field equation and simulation), Brownian motion (due 08.02., 25/100 marks)
• paper presentation (in pairs) on 02.02. (25/100 marks)
  

Selection of papers for the presentations

1. Rebecca and Yu-Xi
   J.L. Lebowitz: From Time-symmetric Microscopic Dynamics to Time-asymmetric Macroscopic Behavior: An Overview (arxiv:0709.0724)
   (leave out section 9)
   
2. E. Valdinoci: From the long jump random walk to the fractional Laplacian (arXiv:0901.3261)
3. Matthew and Pantelis
   J.D. Bancal, R. Pastor-Satorras: Steady-State Dynamics of the Forest Fire Model on Complex Networks (arXiv:0911.0569)
4. D. Foster, J. Foster, M. Paczuski, P. Grassberger: Clustering Phase Transitions and Hysteresis: Pitfalls in Constructing Network Ensembles (arXiv:0911.2055)
5. E. Abad, S.B. Yuste, K. Lindenberg: Reaction-Subdiffusion and Reaction-Superdiffusion Equations for Evanescent Particles Performing Continuous Time Random Walks (arXiv:0911.3137)
6. Chris and Nicolai
   R. Dickmann, R. Vidigal: Quasi-stationary distributions for stochastic processes with an absorbing state (J. Phys. A: Math. Gen. 35 (2002) 1147–1166)
7. Alistair and Sergio
   M. Assaf, B. Meerson: Spectral theory of metastability and extinction in a branching-annihilation reaction (PRE 75, 031122, 2007)
8. Anas and Leigh
   L. Kostal, P. Lansky, J-P. Rospars: Neuronal coding and spiking randomness (Europ. J. of Neuroscience, Vol. 26, pp. 2693–2701, 2007)
9. P. Lamsky, S. Ditlevsen: A review of the methods for signal estimation in stochastic diffusion leaky integrate-and-fire neuronal models (Biol Cybern (2008) 99:253–262)

Matlab and C stuff

• Simple C program for the contact process: contact.c (error with modulo corrected)
  Modified version of the program for Q3.2: contact2.c
  (you might have to adapt the random number generator)
  
• 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
• Frank Kelly: The Mathematics of Traffic in Network
• 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