MA4SP-Stochastic Processes

Module Provider: Mathematics and Statistics
Number of credits: 10 [5 ECTS credits]
Level:7
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.
Co-requisites:
Modules excluded:
Current from: 2023/4

Module Convenor: Dr Jochen Broecker
Email: j.broecker@reading.ac.uk

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.

Aims:

ÌýThis module develops the mathematical theory of stochastic processes in discrete 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 measure theoretic probability;


• Students will understand the concept of Martingales as well as their basic properties;


• Students will understand the concept of Markov processes as well as their basic properties and limit behaviour;

Ìý

Additional outcomes:

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


• Evaluate strategies and decision making inÌýrandomÌýscenarios

Outline content:

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


• Martingales, Limit theorem,ÌýsuccessÌýprobabilities

Brief description of teaching and learning methods:

Tutorials and exercise sheets. Five tutorial meetings of 2 hours each.

Contact hours:

Ìý	Autumn	Spring	Summer
Tutorials		10
Guided independent study:		90
Ìý	Ìý	Ìý	Ìý
Total hours by term	0	100	0
Ìý	Ìý	Ìý	Ìý
Total hours for module	100

Summative Assessment Methods:

Method	Percentage
Written assignment including essay	100

Summative assessment- Examinations:

Summative assessment- Coursework and in-class tests:

A larger assignment over three weeks.

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: /cqsd/-/media/project/functions/cqsd/documents/cqsd-old-site-documents/penaltiesforlatesubmission.pdf
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:

Revision and resubmission of assignment.

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: 10 October 2023