Third-Cycle Courses

Faculty of Engineering | Lund University

Details for the Course Syllabus for Course FMN010F valid from Autumn 2013

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  • English
  • If sufficient demand
  • 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.
  • 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.
Knowledge and Understanding
  • For a passing grade the doctoral student must
  • have a good understanding of the difference between stochastic and deterministic equations, and of Monte Carlo methods for stochastic simulation.
    be able to analyse basic methods for stochastic differential equations, such as the Euler-Maruama and Milstein methods, and more general Runga-Kutta methods.
    have a good understanding of weak and strong convergence, and of stability theory for stochastic differential equations.
    be able to interpret stochastic differential equations and to give examples of models that include them.
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.
Judgement and Approach
  • For a passing grade the doctoral student must
Types of Instruction
  • Lectures
  • Project
Examination Formats
  • Oral exam
  • Seminars given by participants
  • Failed, pass
Admission Requirements
Assumed Prior Knowledge
  • FMNN10 Numerical Methods for Differential Equations, Probability Theory.
Selection Criteria
  • Averina, Tatjana A.: Numerical analysis of systems of ordinary and stochastic differential equations. V.S.P. International Science, 1997. ISBN 9789067642507.
Further Information
  • The course is given if at least five postgraduate students apply. However, there may be some months' delay.
Course code
  • FMN010F
Administrative Information
  •  -09-15
  • FN1/Anders Gustafsson

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