5XÉçÇøÊÓƵ

Random processes (L.7) (862G1)

15 credits, Level 7 (Masters)

Spring teaching

The second module concerned with the notion of a random (stochastic) process, after the Probability Models module.

In this module you will expand the tools you learned in Probability Models to the study of such processes in continuous time (as opposed to discrete time).  The notion of continuous-time Markov chains in a discrete state space is central to the lecture and offers a wide range of applications. The first part of the module focuses on counting processes:  stochastic processes counting the number of occurrences of a type of events (number of buses arriving at a bus stop, number of births in a population).

In the last part of the module, stochastic processes valued in continuous state spaces are introduced, focusing on the family of Gaussian processes. The Brownian motion is a key example which is as important, by the range of its applicability, as the notion of normal variable.

The module will also help you develop further your modelling skills.

Questions may include:

• How can we model a certain problem using a continuous-time Markov chain or a Gaussian process?
• Can we understand how events are correlated at different times?
• Can the model be used to estimate probabilities, expected values, waiting times etc. If so, how?
• How can we understand what happens to the model over a very long interval of time?

Contact hours and workload

This module is approximately 150 hours of work. This breaks down into about 33 hours of contact time and about 117 hours of independent study. The 5XÉçÇøÊÓƵ may make minor variations to the contact hours for operational reasons, including timetabling requirements.

We regularly review our modules to incorporate student feedback, staff expertise, as well as the latest research and teaching methodology. We’re planning to run these modules in the academic year 2024/25. However, there may be changes to these modules in response to feedback, staff availability, student demand or updates to our curriculum.

We’ll make sure to let you know of any material changes to modules at the earliest opportunity.