# DEGREE REGULATIONS & PROGRAMMES OF STUDY 2015/2016

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# Undergraduate Course: Stochastic Differential Equations (MATH10085)

 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 This course provides an introduction to stochastic differential equations (SDEs) emphasising solution techniques and applications over more formal aspects. It focusses on the (Ito) calculus of SDEs and on its application to the exact and numerical solution of SDEs. The assessment consists of 5% CA (5 assignments) and 95% examination. Course description Stochastic 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 course introduces theoretical concepts, including the definition of Brownian motion and stochastic integrals, discusses analytical techniques for the solution of SDEs, and applies these to widely used equations. Numerical methods for both strong and weak approximations of solutions are studied. The course also emphasises the connections between SDEs and partial differential equations. Throughout the course, an intuitive understanding is supported by the presentation of computer demonstrations. 1. Brownian motion: random walks, Wiener process, white noise 2. Stochastic integrals: definition and properties 3. SDEs: definitions, properties and solvable examples 4. Numerical methods: strong and weak convergence, Euler-Maruyama and Milstein schemes 5. Connections with partial differential equations
 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
 Pre-requisites None High Demand Course? Yes
 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 Exam Information Exam Diet Paper Name Hours & Minutes Main Exam Diet S2 (April/May) Stochastic Differential Equations (MATH10085) 2:00
 On completion of this course, the student will be able to: Understanding the concepts of Brownian motion and white noise.Ability to manipulate and solve simple SDEs.Understanding the relationship between SDEs and PDEs.Familiarity with standard numerical algorithms for the solution of SDEs.Solve problems in SDEs that require additional insight beyond seen examples
 L C Evans, An introduction to stochastic differential equations, AMS (2013).
 Graduate Attributes and Skills Not entered Keywords SDE
 Course organiser Dr Jacques Vanneste Tel: (0131 6)50 6483 Email: J.Vanneste@ed.ac.uk Course secretary Mrs Alison Fairgrieve Tel: (0131 6)50 5045 Email: Alison.Fairgrieve@ed.ac.uk
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