MAT-55216 Topics in Applied Mathematics, 3 credits (2012)

Project Work

General instructions

Each student should select a project work topic from the list below and report it to the teacher latest on November 30th. You can ask for more information about the topics from the lecturer. There might also need a possibility to arrange a discussion on that week (to be confirmed). Also note the the last topic is "Own Topic" and the best project work would be one where you apply the methods to an application within your own research area.

  • The project work should be returned to the lecturer ( by e-mail in PDF form latest on December 31st.
  • The document should contain:
    1. Introduction, which explains the research problem in informal terms.
    2. Theory section which describes the theory behind the application/method and cites the relevant books and scientific articles, where the theory can be found.
    3. Simulation/results section, where the method is applied to a simulated or real application.
    4. Summary section, which summarizes the results.


Potential topics include, but are not limited to:

  1. Stochastic Runge-Kutta methods
  2. Strong and weak convergence of numerical methods
  3. Numerical simulation of SDEs
  4. Gaussian approximations of SDEs
  5. Variational Bayes approximations of SDEs
  6. Series expansions of SDEs
  7. Small noise expansion approximations
  8. Numerical solution of Fokker-Planck-Kolmogorov equations
  9. Solution of PDEs with Feynman-Kac
  10. Wiener/Feynman path integrals and SDEs
  11. Existence and uniqueness of SDEs
  12. Martingale representation theorem
  13. Analytical solutions of SDEs
  14. Kalman-Bucy filter
  15. Kushner and Zakai equations
  16. Continuous-time filtering theory
  17. Continuous-discrete filtering theory
  18. Levy-process driven SDEs
  19. Spatially distributed systems
  20. Black-Scholes formula
  21. Physics application
  22. Biological application
  23. Communications application
  24. Financial application
  25. Other application
  26. Own topic