MA4SP-Stochastic Processes

Module Provider: Mathematics and Statistics
Number of credits: 10 [5 ECTS credits]
Terms in which taught: Spring term module
Pre-requisites: MA3MTI Measure Theory and Integration
Non-modular pre-requisites: Part 3 students wishing to select this module must either take MA3MTI as a co-requisite, or must demonstrate equivalent knowledge and seek approval from the module convenor.
Modules excluded:
Current from: 2020/1

Module Convenor: Dr Jochen Broecker


Type of module:

Summary module description:

Stochastic processes and probability are important tools in applications and many areas of pure mathematics, but also objects of study in their own right.


This module develops the mathematical theory of stochastic processes and probability in in discrete and continuum time and their properties in a rigorous manner.

Assessable learning outcomes:

On completion of this module students will have acquired:

  • Students will understand basic concepts of  probabilityStudents will understand the concept of stochastic processes and in particular Martingale theory;

  • Students will be able to consider rigorously different classes of discrete processes and their properties. In particular limit theorems.


Additional outcomes:

  • Use the acquired techniques to study non trivial general properties of  processes;

  • Evaluate strategies and decision making in random scenarios

Outline content:

  • Basic concepts of probability including: probability measures, push forward measures and distributions, product measure and independence

  • Martingales, Limit theorem, success probabilities

Brief description of teaching and learning methods:
Lectures with tutorials and exercise sheets.

Contact hours:
  Autumn Spring Summer
Lectures 20
Tutorials 4
Guided independent study: 76
Total hours by term 100
Total hours for module 100

Summative Assessment Methods:
Method Percentage
Written exam 60
Set exercise 40

Summative assessment- Examinations:

2 hours

Summative assessment- Coursework and in-class tests:

A number of assignments.

Formative assessment methods:
Problem Sheets.

Penalties for late submission:

The Support Centres will apply the following penalties for work submitted late:

  • where the piece of work is submitted after the original deadline (or any formally agreed extension to the deadline): 10% of the total marks available for that piece of work will be deducted from the mark for each working day (or part thereof) following the deadline up to a total of five working days;
  • where the piece of work is submitted more than five working days after the original deadline (or any formally agreed extension to the deadline): a mark of zero will be recorded.
The University policy statement on penalties for late submission can be found at:
You are strongly advised to ensure that coursework is submitted by the relevant deadline. You should note that it is advisable to submit work in an unfinished state rather than to fail to submit any work.

Assessment requirements for a pass:
A mark of 50% overall.

Reassessment arrangements:

One examination of 2 hours duration  in August/September - the resit module mark will be the higher of the exam mark (100% exam) and the exam mark plus previous coursework marks (60% exam, 40% coursework).

Additional Costs (specified where applicable):
1) Required text books:
2) Specialist equipment or materials:
3) Specialist clothing, footwear or headgear:
4) Printing and binding:
5) Computers and devices with a particular specification:
6) Travel, accommodation and subsistence:

Last updated: 26 January 2021


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