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MA933 - Stochastic Modelling and Random Processes (15 CATS)

Lecturer: Susana Gomes for 23/24

Students who are not in the MathSys CDT who wish to take this module should contact the module leader before registering. Registering on eVision/online does not guarantee you a place on the module.

Module Aims

This is one of 4 core taught modules for the MSc in Mathematics of Systems. The main aims are to provide a broad background in theory and applications of complex networks and random processes, and related practical and computational skills to use these techniques in applied mathematical research and modelling. Students will become familiar with basic network theoretic definitions, commonly used network statistics, probabilistic foundations of random processes, some commonly studied Markov processes/chains, and the links between these topics through random graph theory.


  1. Review of important concepts from Probability
  2. Discrete-time Markov chains
  3. Continuous-time Markov chains
  4. Stochastic models of interacting processes (including population dynamics, epidemics)
  5. Scaling limits and diffusion processes
  6. Basic network definitions and statistics
  7. The Erdos-Renyi random graph and connection to percolation
  8. Heterogeneous network models
  9. Spatial network models

Illustrative Bibliography

Handbook of Stochastic Methods, CW Gardiner, Springer 2004.
Networks: An Introduction, MEJ Newman, OUP 2010.
Probability and Random Processes (3rd ed.), G Grimmett and D Stirzaker, OUP 2001.
Random Graph Dynamics, R Durrett, CUP 2007.


  • Per week: 3 hours of lectures, 1 hour of classes
  • Classes are usually held on Tuesdays 10:00 - 12:00 and Fridays 10:00 - 12:00, although this is subject to change. Classes are held in D1.07 (Complexity Seminar Room), Floor 1, Zeeman Building, unless otherwise advised.
  • Duration: 10 weeks (term 1)


For deadlines see Module Resources page

  • Class test (80%)
  • Homework assignments (20%)