Stochastic Processes module (MA51005)

About the module

This module, aimed at Level 5 students, gives an introduction to stochastic processes, considering the theory of random variables, Markov chains and going on to some continuous-time stochastic processes. MA51007 Measure Theory (or equivalent) are a prerequisite. This module may optionally be taken in combination with others by Level 5 students taking the MMath in Mathematics or the MSci in Mathematical Biology or Mathematics and Physics. If you have questions about this module or the possible combinations, please contact your Adviser of Studies.

Prerequisites

Students taking this module would find it beneficial to have taken the module MA51007 Measure Theory, or equivalent.

Indicative Content

• Probability space and Random Variables

  Representations of probability measures, moments, law of large numbers, central limit theorem, operations and transformations of random variables, applications.

• Markov chains

  the Markov property, ergodic theorem and invariant measures, first passage time, discrete random walks, applications

• Brownian motion

  Brownian motion as the continuous limit of a random walk, Gaussian processes, Mean-square calculus of random processes, introduction to Stochastic Differential Equations, applications

Delivery and Assessment

The module will be assessed by written mathematical problems in which the students are required to adapt and apply the methods that they have learned in order to solve the problems.

Credit Rating

This module is a Scottish Higher Education Level 5 or SCQF level 11 module and is rated as 15 SCOTCAT credits or 7.5 ECTS credits.