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MA933 - Stochastic Modelling and Random Processes (15 Cats)

Lecturer: Stefan Grosskinsky (Mathematics and Complexity)

Module Aims

This is one of 4 core modules for the new 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.

Syllabus

  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 Stirzakek, OUP 2001.
Random Graph Dynamics, R Durrett, CUP 2007.

Teaching

See main calendar for timetable

  • Per week: 3 hours of lectures, 1 hour of classes
  • Duration: 10 weeks (term 1)

Assessment

For deadlines see Module Resources page

  • Written homework assignments (20%)
  • Written class test (80%)