# DEGREE REGULATIONS & PROGRAMMES OF STUDY 2018/2019

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# Undergraduate Course: Applied Stochastic Differential Equations (MATH10053)

 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.
 Pre-requisites Co-requisites Prohibited Combinations Students MUST NOT also be taking Simulation (MATH10015) AND Stochastic Differential Equations (MATH10085) AND Numerical Methods for Stochastic Differential Equations (MATH11156) 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.
 Pre-requisites None High Demand Course? Yes
 Academic year 2018/19, 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 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 ) Assessment (Further Info) Written Exam 50 %, Coursework 50 %, Practical Exam 0 % Additional Information (Assessment) 50% continuous assessment 50% examination Feedback Not entered Exam Information Exam Diet Paper Name Hours & Minutes Main Exam Diet S1 (December) MATH10053 Applied Stochastic Differential Equations 2:00
 On completion of this course, the student will be able to: Define Brownian motion and stochastic integral.Manipulate and solve simple SDEs.Write numerical algorithms in MATLAB for the solution of SDEs based on the Euler and Milstein's methods.Identify long time properties of Markov processes.
 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)
 Graduate Attributes and Skills Not entered Keywords ASDE,probability,numerical methods
 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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