Each student should select a project work topic from the list below and report it via the mailbox below latest on December 8th. You can ask for more information about the topics from the lecturers. 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 document should be returned to the lecturer (firstname.lastname@example.org) via MyCourses (below) latest on January 8th, 2017.
The document should contain:
- Introduction, which explains the research problem in informal terms.
- Theory section which describes the theory behind the application/method and cites the relevant books and scientific articles, where the theory can be found.
- Simulation/results section, where the method is applied to a simulated or real application.
- Summary section, which summarizes the results.
Potential topics include, but are not limited to:
- Strong and weak convergence of numerical methods
- Parameter estimation in SDEs
- Exact simulation of SDEs
- Variational Bayes approximations of SDEs
- Series expansions of SDEs
- Small noise expansion approximations
- Numerical solution of Fokker-Planck-Kolmogorov equations
- State-space methods for Gaussian processes
- Solution of PDEs with Feynman-Kac
- Wiener/Feynman path integrals and SDEs
- Existence and uniqueness of SDEs
- Martingale representation theorem
- Analytical solutions of SDEs
- Non-linear Kalman-Bucy filtering
- Kushner and Zakai equations
- Continuous-time filtering theory
- Continuous-discrete filtering theory
- Levy-process driven SDEs
- Spatially distributed systems
- Black-Scholes formula
- Physics application
- Biological application
- Communications application
- Navigation application
- Own topic