Not available in 2020/21
MA414      Half Unit
Stochastic Analysis

This information is for the 2020/21 session.

Teacher responsible

Dr Arne Lokka


This course is available on the MSc in Applicable Mathematics and MSc in Financial Mathematics. This course is available with permission as an outside option to students on other programmes where regulations permit.


ST409 or MA411.

Course content

This course is concerned with a rigorous introduction to the area of stochastic analysis with emphasis on Itô calculus. The course begins necessary preliminaries, followed by a construction of the standard Brownian motion and a study of its properties. Subsequently, Lévy’s characterisation of Brownian motion, martingale representation theorems and Girsanov’s theorem are established. The course then expands on a study of stochastic differential equations.


20 hours of lectures and 10 hours of seminars in the LT.

Indicative reading

Full lecture notes will be provided. The following may prove useful: I Karatzas and S E Shreve, Brownian Motion and Stochastic Calculus, Springer; B Øksendal, Stochastic Differential Equations: An Introduction with Applications, Springer; D Revuz and M Yor, Continuous Martingales and Brownian Motion, Springer; L C G Rogers and D Williams, Diffusions, Markov Processes, and Martingales, Cambridge.


Exam (100%, duration: 2 hours) in the summer exam period.

Important information in response to COVID-19

Please note that during 2020/21 academic year some variation to teaching and learning activities may be required to respond to changes in public health advice and/or to account for the situation of students in attendance on campus and those studying online during the early part of the academic year. For assessment, this may involve changes to mode of delivery and/or the format or weighting of assessments. Changes will only be made if required and students will be notified about any changes to teaching or assessment plans at the earliest opportunity.

Key facts

Department: Mathematics

Total students 2019/20: 7

Average class size 2019/20: 7

Controlled access 2019/20: No

Value: Half Unit

Guidelines for interpreting course guide information

Personal development skills

  • Self-management
  • Problem solving
  • Application of information skills
  • Communication
  • Application of numeracy skills
  • Specialist skills