Topic outline

  • Project work overview

    • Select your favorite topic e.g. from the coursebook among the topics which have not been covered on the course. However, you can also think of an application of SDE methods in your own research or application.
    • Write around 5-10 pages report which contains a brief review of the theory and then a numerical illustration. That is, a short technical report/article on the subject.
    • Deadlines are 26.7.2020 (topic) and 28.8.2020 (final report)

    Project topics

    • Strong and weak convergence of numerical methods
    • Exact simulation of SDEs
    • Lamperti transform
    • Doob’s h-transform
    • Girsanov theorem
    • 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
    • Taylor series expansions of moment equations
    • Levy-process driven SDEs
    • Spatially distributed systems
    • Black-Scholes formulae
    • Physics application
    • Biological application
    • Communications application
    • Navigation application
    • Own topic

    Project work report

    The report should be returned in PDF form below by 28.8.2020 and it should contain at least the following:

    • Introduction. Explains the research problem in informal terms. Based on this, a fellow student on the course should be able to understand how your project relates to the rest of the course.
    • Theory (Materials and Methods). Describes the theory behind the application and/or methodology and cites books and scientific articles, where the theory can be found.
    • Simulation/Results. The method is applied to a simulated or real application. Codes can be included as appendices, if necessary.
    • Summary (Discussion and Conclusion). Summarizes the results and provides insight into the usability of the method. If applicable, it also discusses the good/bad sides of the approach.
    Codes can be returned as a separate archive or included into the appendix of the report if it is more convenient. 

    Use some word processing software (e.g. [pdf/xe/lua/...]LaTeX, preferably) to typeset your report. You can use some standard article or report template.