## 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:
Current from: 2018/9

Module Convenor: Dr Tobias Kuna

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:

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 probability;

• Students will understand the concept of stochastic processes and in particular Brownian motion;

• 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:

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

• Limit theorem: Law of large numbers and Central limit theorem;

• Construction of Brownian motion;

• Path properties;

• Transformation 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 Oral assessment and presentation 60 Set exercise 40

Summative assessment- Examinations:

Summative assessment- Coursework and in-class tests:

A number of assignments and one oral examination.

Formative assessment methods:
Problem Sheets.

Penalties for late submission:
The Module Convener 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[1] (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.

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

Reassessment arrangements:

An oral examination  in August/September - the resit module mark will be the higher of the oral exam mark (100% oral exam) and the oral exam mark plus previous coursework marks (60% oral 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: 20 April 2018

THE INFORMATION CONTAINED IN THIS MODULE DESCRIPTION DOES NOT FORM ANY PART OF A STUDENT'S CONTRACT.