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DEGREE REGULATIONS & PROGRAMMES OF STUDY 2015/2016

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DRPS : Course Catalogue : School of Mathematics : Mathematics

Undergraduate Course: Stochastic Differential Equations (MATH10085)

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
SummaryStochastic methods, stochastic differential equations (SDEs) in particular, are used extensively in finance, industry and in sciences. Reflecting this, 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; it also emphasises the connections between SDEs and partial differential equations. The second part centres on numerical methods for both strong and weak approximations of solutions and introduces widely used numerical schemes.
Course description Part 1: Introduction to SDEs
- Brownian motion: random walks, Wiener process, white noise.
- Stochastic integrals: definition, Ito isometry, Ito¿s formula
- SDEs: definitions, existence and uniqueness, examples
- Applications: applications to PDEs (Laplace equation, Feynman-Kac), limit of coloured noise (Stratonovich SDEs and conversion rules).

Part 2: Numerical SDEs
- Strong and weak approximations of solutions to SDEs,
- Euler approximations, Milstein scheme,
- Order of accuracy of the approximations,
- Higher order schemes, accelerated convergence,
- Weak approximations of SDEs via numerical solutions of PDEs.
Entry Requirements (not applicable to Visiting Students)
Pre-requisites Students MUST have passed: Honours Differential Equations (MATH10066) AND ( Probability (MATH08066) OR Probability with Applications (MATH08067))
Co-requisites
Prohibited Combinations Students MUST NOT also be taking Simulation (MATH10015)
Other requirements None
Information for Visiting Students
Pre-requisitesNone
Course Delivery Information
Academic year 2015/16, Available to all students (SV1) Quota:  None
Course Start Semester 2
Timetable Timetable
Learning and Teaching activities (Further Info) Total Hours: 100 ( Lecture Hours 22, Seminar/Tutorial Hours 5, Summative Assessment Hours 2, Programme Level Learning and Teaching Hours 2, Directed Learning and Independent Learning Hours 69 )
Assessment (Further Info) Written Exam 95 %, Coursework 5 %, Practical Exam 0 %
Additional Information (Assessment) Coursework 5%, Examination 95%
Feedback Not entered
No Exam Information
Learning Outcomes
Understanding the concepts of Brownian motion and white noise.
Ability to manipulate and solve simple SDEs.
Understanding the relationship between SDEs and parabolic PDEs.
Understanding the concept of strong and weak approximations to solutions of SDEs.
Familiarity with standard numerical algorithms for the solution of SDEs.
Appreciation of the challenges posed by accurate numerical solutions of SDEs.
Reading List
L C Evans, An introduction to stochastic differential equations, AMS (2013).
Additional Information
Graduate Attributes and Skills Not entered
KeywordsSDE
Contacts
Course organiserDr Jacques Vanneste
Tel: (0131 6)50 6483
Email:
Course secretaryMrs Alison Fairgrieve
Tel: (0131 6)50 5045
Email:
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