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 | Stochastic differential equations (SDEs) are used extensively in finance, industry and in sciences. This course provides an introduction to SDEs that discusses the fundamental concepts and properties of SDEs and presents strategies for their exact, approximate, and numerical solution.
The first part of the course focuses on theoretical concepts, including the definition of Brownian motion and stochastic integrals, and on analytical techniques for the solution of SDEs. The second part centres on numerical methods for both strong and weak approximations of solutions and introduces widely used numerical schemes. The last part of the course concentrates on identifying the long time properties of solutions of SDEs. |
| Course description |
Probability Theory and Random Variables
Stochastic Processes: Basic Definitions, Brownian motion, stationary processes, Ornstein Uhlenbeck process, The Karhunen-Loeve expansion.
Markov and diffusion processes: Chapman-Kolmogorov equations, generator of a Markov Process and its adjoint, ergodic and stationary Markov processes, Fokker Planck Equation, connection between diffusion processes and SDEs.
Elements of Numerical Analysis of SDEs.
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Entry Requirements (not applicable to Visiting Students)
| Pre-requisites |
|
Co-requisites | |
| Prohibited Combinations | Students MUST NOT also be taking
Simulation (MATH10015) AND
Stochastic Differential Equations (MATH10085)
|
Other requirements | Students not on the MSc in Computational Applied Mathematics programme MUST have passed (Probability MATH08066 or Probability with Applications MATH08067) and Honours Differential Equations MATH10066. |
Information for Visiting Students
| Pre-requisites | None |
| High Demand Course? |
Yes |
Course Delivery Information
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| Academic year 2020/21, 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 5,
Supervised Practical/Workshop/Studio Hours 6,
Summative Assessment Hours 2,
Programme Level Learning and Teaching Hours 2,
Directed Learning and Independent Learning Hours
63 )
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| Assessment (Further Info) |
Written Exam
50 %,
Coursework
50 %,
Practical Exam
0 %
|
| Additional Information (Assessment) |
50% continuous assessment
50% examination
There would be 2 pieces of coursework each one counting for 25% of the total mark. The first one will be made available in the beginning of week 4 and will be due at the end of week 6, while the second coursework will be made available in the beginning of week 8 and will be due at the end of week 10.
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| Feedback |
Students will receive detailed feedback within 2 weeks of submitting their assignment. This will include model solutions for the questions, as well as short video recordings containing code demonstrations explaining the more computational aspects of the assignments. |
| 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:
- Use definitions and results from the course to deduce properties of Brownian motion and the stochastic integral.¿¿
- Manipulate and solve simple SDEs.¿
- Work in a sustained way on a longer problem involving ideas from the course.
- Write numerical algorithms in Python for the solution of SDEs based on the Euler and¿Milstein's methods.¿
- Write numerical algorithms in Python for the solution of SDEs based on the Euler and¿Milstein's methods.¿
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Reading List
G.A. Pavliotis, Stochastic Processes and Applications, Springer (2014) (recommended)
L C Evans, An introduction to stochastic differential equations, AMS (2013) (reference)
P E Kloeden & E Platen, Numerical solutions of stochastic differential equations, 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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