Markov Chains Michaelmas 2025 syllabus
Below is the range of topics covered in the course; it may change from year to year.
Syllabus:
- Definition of a Markov chain.
- Basic properties.
- Powers of the transition matrix.
- Communicating classes.
- Hitting times.
- Strong Markov property.
- Transience and recurrence.
- Random walks on \( \mathbb{Z}^d \).
- Invariant distribution.
- Time reversibility.
- Convergence to equilibrium.
- Ergodic theorem.