STU34503 – Stochastic Models in Space and Time I

Module CodeSTU34503
Module Name Stochastic Models in Space and Time I
ECTS Weighting[1]5 ECTS
Semester taughtSemester 1
Module Coordinator/s Dr. Jason Wyse

Module Learning Outcomes

On successful completion of this module, students will be able to:

  • LO1. Discuss and model everyday examples of stochastic processes
  • LO2. Define and apply the Markov property
  • LO3. Describe long run properties of Markov chains
  • LO4. Deal with simple Markov processes in continuous time

Module Content

Specific topics addressed in this module include:

  • Examples of stochastic processes
  • The Markov property and discrete state space Markov chains
  • Chapman-Kolmogorov equation
  • Convergence to stable distribution
  • Poisson processes and their properties and applications
  • Further discrete state space Markov processes
  • Brownian motion and geometric Brownian motion

Teaching and learning Methods

Classes will be available online (3 sessions per week). Some sessions will focus on problem sets.

Assessment Details

Assessment ComponentBrief Description Learning Outcomes Addressed% of totalWeek setWeek Due
ExamTake-Home ExamLO1, LO2, LO3, LO490%TBC
AssignmentsFour assignments throughout semesterLO1, LO2, LO3, LO410%TBC

Reassessment Details

100% Take-Home Exam  

Contact Hours and Indicative Student Workload

Contact Hours (scheduled hours per student over full module), broken down by: 33 hours
Lecture
29 hours
Laboratory0 hours
Tutorial or seminar4 hours
Other0 hours
Independent study (outside scheduled contact hours), broken down by:82 hours
Preparation for classes and review of material (including preparation for examination, if applicable42 hours
completion of assessments (including examination, if applicable)40 hours
Total Hours115 hours

Recommended Reading List

A comprehensive text which is a good companion for this module and beyond is

  • “Markov Chains (Cambridge Series in Statistical and Probabilistic Mathematics)” by J.R. Norris.

An excellent text (one for the bookshelf) to study essential probability concepts including Markov Chains is

  • “An Introduction to Probability Theory and Its Applications” by W. Feller.

A nice text with lots of engaging examples is (the author hosts a PDF of an old edition on his webpage)

  • “Essentials of Stochastic Processes” by R. Durrett.

It is not compulsory to buy any of these texts. It is intended that notes provided in class should be sufficient to study for the purposes of this module.

Module Pre-requisites

Prerequisite modules: STU23501 and STU23502

Other/alternative non-module prerequisites: NA

Module Co-requisites

None

Module Website

Blackboard