|Module Name||Stochastic Models in Space and Time I|
|ECTS Weighting||5 ECTS|
|Semester taught||Semester 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
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 Component||Brief Description||Learning Outcomes Addressed||% of total||Week set||Week Due|
|Exam||Take-Home Exam||LO1, LO2, LO3, LO4||90%||TBC|
|Assignments||Four assignments throughout semester||LO1, LO2, LO3, LO4||10%||TBC|
100% Take-Home Exam
Contact Hours and Indicative Student Workload
|Contact Hours (scheduled hours per student over full module), broken down by:||33 hours|
|Tutorial or seminar||4 hours|
|Independent study (outside scheduled contact hours), broken down by:||82 hours|
|Preparation for classes and review of material (including preparation for examination, if applicable||42 hours|
|completion of assessments (including examination, if applicable)||40 hours|
|Total Hours||115 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.
Prerequisite modules: STU23501 and STU23502
Other/alternative non-module prerequisites: NA