Undergraduate Course: Applied Stochastic Differential Equations (MATH10053)
Course Outline
| School | School of Mathematics |
College | College of Science and Engineering |
| Credit level (Normal year taken) | SCQF Level 10 (Year 4 Undergraduate) |
Availability | Available to all students |
| SCQF Credits | 10 |
ECTS Credits | 5 |
| Summary | Many systems include some unpredictability, and this unpredictability is typically modelled through the addition of "noise". Stochastic differential equations are a generalization of ordinary differential equations, allowing an additional noise term to be introduced.
This course introduces stochastic differential equations. Starting first from their definition, through the introduction of the Ito stochastic integral, the course develops techniques for studying the properties of the stochastic processes defined by these equations, and considers the analytic solution of some simple cases. The course further introduces numerical methods which can be used to seek approximate solutions, describing how to define the numerical error in a numerical approximation of a stochastic process. The course further considers links between stochastic differential equations and partial differential equations. |
| Course description |
Syllabus:
- Gaussian processes
- Brownian motion
- Ito and Stratonovich stochastic differential equations
- Ito's formula
- Numerical methods, including the Euler-Maruyama and Milstein schemes
- Linking to partial differential equations
The course will make use of Python.
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Information for Visiting Students
| Pre-requisites | Visiting students are advised to check that they have studied the material covered in the syllabus of each pre-requisite course before enrolling. |
| High Demand Course? |
Yes |
Course Delivery Information
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| Academic year 2024/25, Available to all students (SV1)
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Quota: None |
| Course Start |
Semester 1 |
Timetable |
Timetable |
| Learning and Teaching activities (Further Info) |
Total Hours:
100
(
Lecture Hours 22,
Seminar/Tutorial Hours 9,
Summative Assessment Hours 2,
Programme Level Learning and Teaching Hours 2,
Directed Learning and Independent Learning Hours
65 )
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| Assessment (Further Info) |
Written Exam
80 %,
Coursework
20 %,
Practical Exam
0 %
|
| Additional Information (Assessment) |
Coursework 20% , Exam 80%
|
| Feedback |
Not entered |
| Exam Information |
| Exam Diet |
Paper Name |
Hours & Minutes |
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| Main Exam Diet S1 (December) | Applied Stochastic Differential Equations MATH10053 | 2:120 | |
Learning Outcomes
On completion of this course, the student will be able to:
- Use definitions and results from the course to deduce properties of Brownian motion.
- Derive properties of stochastic processes defined by stochastic differential equations.
- Manipulate and solve simple stochastic differential equations.
- Find approximate solutions to stochastic differential equations using numerical methods, implemented in the Python programming language.
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Reading List
An introduction to stochastic differential equations, Lawrence C Evans, AMS (2013) (recommended)
Stochastic Processes and Applications, Grigorios A. Pavliotis, Springer (2014) (reference)
Numerical solutions of stochastic differential equations, Peter E Kloeden & Eckhard Platen, Springer (1999) (reference) |
Additional Information
| Graduate Attributes and Skills |
Not entered |
| Keywords | ASDE,probability,numerical methods |
Contacts
| Course organiser | Dr Kostas Zygalakis
Tel: (0131 6)50 5975
Email: K.Zygalakis@ed.ac.uk |
Course secretary | Mrs Alison Fairgrieve
Tel: (0131 6)50 5045
Email: Alison.Fairgrieve@ed.ac.uk |
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