## 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: MA4MTI can be taken as a co-requisite in place of MA3MTI
Co-requisites:
Modules excluded:
Module version for: 2017/8

Module Convenor: Dr Tobias Kuna

Summary module description:

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

Aims:

This module develops the mathematical theory of stochastic processes 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 the concept of stochastic processes and in particular Brownian motion;

• Students will be able to evaluate and derive path properties, stochastic and asymptotic properties of processes;

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

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

• Interrelation between transformation, path properties and transformation of processes.

Outline content:

• Construction of Brownian motion;

• Path properties;

• Transformation of processes;

• Markov property;

• Asymptotic properties of processes.

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 100.00 Total hours for module 100.00

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

Other information on summative assessment:
A number of assignments and one examination.

Formative assessment methods:
Problem Sheets.

Penalties for late submission:
The Module Convenor will apply the following penalties for work submitted late, in accordance with the University policy.

• where the piece of work is submitted up to one calendar week after the original deadline (or any formally agreed extension to the deadline): 10% of the total marks available for the 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: http://www.reading.ac.uk/web/FILES/qualitysupport/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.

Length of examination:
2 hours.

Requirements for a pass:
A mark of 50% overall.

Reassessment arrangements:
One examination paper of two 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).