MTH5230 · Markov chains and random walks

Overview

Homogeneous Markov chains in finite and countable state space. Foster-Lyapunov criterion for recurrence and transience. Random walks in one and more dimensions. Polya theorem. Limit theorems: law of iterated logarithms, functional central limit theorem. Connections with the Brownian motion and the heat equation. Applications of random walks to finance and insurance.

Offerings

Assessment

The Handbook lists an examination for this unit.

Assessment details may change. Please refer to the assessment information in Moodle closer to the start of the teaching period.

Requisites

The Handbook lists no prerequisite, corequisite or prohibition for this unit.

Learning outcomes

1. Develop specialised mathematical knowledge and skills within the theories of markov chains and random walks.
2. Apply sophisticated stochastic modelling skills within a variety of contexts, from a wide range of scientific areas of knowledge.
3. Apply critical thinking to problems in Markov chains in general, and in the theory of random walks in particular.
4. Formulate expert solutions to practical financial, engineering or scientific problems using specialised cognitive and technical skills within the theories of markov chains and random walks.

Workload

• Two 1.5-hour seminars; • One 1-hour applied class (in weeks 2-12) and • Eight hours of independent study per week.

Student experience, not official rules. Nothing here changes what the Handbook says.