Valid from: Autumn 2013
Decided by: FN1/Anders Gustafsson
Date of establishment: 2014-09-15
Division: Numerical Analysis
Course type: Third-cycle course
Teaching language: English
Stochastic differential equations are increasingly important in many cutting-edge models in physics, biochemistry and finance. The aim of the course is to give the postgraduate student a fundamental knowledge and understanding of stochastic differential equations, emphasizing the computational techniques necessary for stochastic simulation in modern applications.
Knowledge and Understanding
For a passing grade the doctoral student must
Competences and Skills
For a passing grade the doctoral student must be able to independently implement discretization schemes for stochastic differential equations and critically evaluate the results.
The course is divided into two parts, with the first dealing with classical theory for deterministic ordinary differential equations (ODEs) and the second with theory for stochastic differential equations (SDEs). The deterministic part reviews necessary background, in particular Runge-Kutta and Rosenbrock methods. The second part gives an introduction to SDEs, and presents basic ideas and techniques used in statistical simulation, such as root mean square stability; consistency notions; and weak and strong convergence. A few applications will be studied in more detail, including pertinent problems to be solved using a computer.
Averina, Tatjana A.: Numerical analysis of systems of ordinary and stochastic differential equations. V.S.P. International Science, 1997. ISBN 9789067642507.
Types of instruction: Lectures, project
Examination formats: Oral exam, seminars given by participants
Grading scale: Failed, pass
Assumed prior knowledge: FMNN10 Numerical Methods for Differential Equations, Probability Theory.
The course is given if at least five postgraduate students apply. However, there may be some months' delay.