ST403-15 Brownian Motion

Academic year
21/22
Department
Statistics
Level
Undergraduate Level 4
Module leader
Oleg Zaboronski
Credit value
15
Module duration
10 weeks
Assessment
Multiple
Study location
University of Warwick main campus, Coventry
Introductory description

This module runs in Term 1 and is only available for students with their home department in Statistics. It is delivered by the Mathematics Department under the module code MA4F7.

Prerequisites: ST318 Probability Theory OR MA359 Measure Theory.

In 1827 the Botanist Robert Brown reported that pollen suspended in water exhibit random erratic movement. This ‘physical’ Brownian motion can be understood via the kinetic theory of heat as a result of collisions with molecules due to thermal motion. The phenomenon has later been related in Physics to the diffusion equation, which led Albert Einstein in 1905 to postulate certain properties for the motion of an idealized ‘Brownian particle’ with vanishing mass:

Module web page

Module aims

The module studies the construction and properties of Brownian motion, a fundamental tool for modelling processes which evolve randomly in time. Brownian motion is used widely in many areas of pure and applied mathematics and in the last few decades it has become essential to the study of financial maths as a model of stock prices.

Outline syllabus

This is an indicative module outline only to give an indication of the sort of topics that may be covered. Actual sessions held may differ.

Topics discussed in this module include:

Learning outcomes

By the end of the module, students should be able to:

Indicative reading list

Peter Mörters and Yuval Peres, Brownian Motion, Cambridge University Press, 2010
René L. Schilling and Lothar Partzsch, Brownian motion: an introduction to stochastic processes, De Gruyter, 2014
Thomas M. Liggett, Continuous Time Markov Processes - An Introduction, AMS Graduate studies in Mathematics 113, 2010

View reading list on Talis Aspire

Subject specific skills

At the end of the module students will be able to :

Transferable skills

Students will acquire key reasoning and problem solving skills which will empower them to address new problems with confidence.

Study time

Type Required Optional
Lectures 30 sessions of 1 hour (20%) 2 sessions of 1 hour
Tutorials 9 sessions of 1 hour (6%)
Private study 111 hours (74%)
Total 150 hours
Private study description

Review lectured material and work on set exercises.

Costs

No further costs have been identified for this module.

You do not need to pass all assessment components to pass the module.

Students can register for this module without taking any assessment.

Assessment group D1
Weighting Study time
Assignments worth 15% 15%

Coursework

On-campus Examination 85%

The examination paper will contain five questions, of which the mark from the FIRST question and the best marks of THREE of the remaining four questions will be used to calculate your grade.

~Platforms - Moodle


  • Answerbook Gold (24 page)
Assessment group R
Weighting Study time
Online Examination 100%

The examination paper will contain five questions, of which the mark from the FIRST question and the best marks of THREE of the remaining four questions will be used to calculate your grade.

~Platforms - Moodle

Feedback on assessment

Marked coursework and exam feedback

Past exam papers for ST403

Courses

This module is Optional for:

  • Year 1 of TMAA-G1PE Master of Advanced Study in Mathematical Sciences
  • Year 1 of TIBS-N3G1 Postgraduate Taught Financial Mathematics
  • Year 1 of TMAA-G1P9 Postgraduate Taught Interdisciplinary Mathematics
  • Year 1 of TMAA-G1P0 Postgraduate Taught Mathematics
  • USTA-G300 Undergraduate Master of Mathematics,Operational Research,Statistics and Economics
    • Year 3 of G300 Mathematics, Operational Research, Statistics and Economics
    • Year 4 of G300 Mathematics, Operational Research, Statistics and Economics

This module is Option list A for:

  • Year 4 of USTA-G300 Undergraduate Master of Mathematics,Operational Research,Statistics and Economics
  • Year 5 of USTA-G301 Undergraduate Master of Mathematics,Operational Research,Statistics and Economics (with Intercalated
  • Year 4 of USTA-G1G3 Undergraduate Mathematics and Statistics (BSc MMathStat)
  • Year 5 of USTA-G1G4 Undergraduate Mathematics and Statistics (BSc MMathStat) (with Intercalated Year)

This module is Option list B for:

  • Year 4 of UCSA-G4G3 Undergraduate Discrete Mathematics

This module is Option list D for:

  • Year 4 of USTA-G300 Undergraduate Master of Mathematics,Operational Research,Statistics and Economics
  • Year 5 of USTA-G301 Undergraduate Master of Mathematics,Operational Research,Statistics and Economics (with Intercalated

This module is Option list E for:

  • Year 4 of USTA-G300 Undergraduate Master of Mathematics,Operational Research,Statistics and Economics
  • Year 5 of USTA-G301 Undergraduate Master of Mathematics,Operational Research,Statistics and Economics (with Intercalated