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DRPS : Course Catalogue : School of Mathematics : Mathematics

Undergraduate Course: Applied Stochastic Differential Equations (MATH10053)

Course Outline
SchoolSchool of Mathematics CollegeCollege of Science and Engineering
Credit level (Normal year taken)SCQF Level 10 (Year 4 Undergraduate) AvailabilityAvailable to all students
SCQF Credits10 ECTS Credits5
SummaryMany 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.
Entry Requirements (not applicable to Visiting Students)
Pre-requisites Students MUST have passed: Computing and Numerics (MATH08065) AND Probability (MATH08066) AND Honours Differential Equations (MATH10066)
Prohibited Combinations Students MUST NOT also be taking Simulation (MATH10015) AND Stochastic Differential Equations (MATH10085)
Other requirements Students on the MSc in Computational Applied Mathematics programme need not satisfy the pre-requisites, but should note the required background.
Information for Visiting Students
High Demand Course? Yes
Course Delivery Information
Academic year 2023/24, Available to all students (SV1) 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 )
Assessment (Further Info) Written Exam 80 %, Coursework 20 %, Practical Exam 0 %
Additional Information (Assessment) Coursework 20% , Exam 80%

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Exam Information
Exam Diet Paper Name Hours & Minutes
Main Exam Diet S1 (December)2:00
Learning Outcomes
On completion of this course, the student will be able to:
  1. Use definitions and results from the course to deduce properties of Brownian motion.
  2. Derive properties of stochastic processes defined by stochastic differential equations.
  3. Manipulate and solve simple stochastic differential equations.
  4. Find approximate solutions to stochastic differential equations using numerical methods, implemented in the Python programming language.
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
KeywordsASDE,probability,numerical methods
Course organiserDr James Maddison
Tel: (0131 6)50 5036
Course secretaryMrs Alison Fairgrieve
Tel: (0131 6)50 5045
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