401-4926-13L Stochastic Filtering - Theory and Applications
|Semester||Autumn Semester 2015|
|Language of instruction||English|
|Abstract||Theory and practice of linear and non-linear filtering with applications in statistics and finance.|
|Objective||Theory and practice of linear and non-linear filtering with applications in statistics and finance.|
|Content||Filtering is the task of recovering unobserved state variables from noisy observations. This course covers the theoretical foundations of filtering in various levels of generality, as well as numerics and applications in statistics and finance.|
The course starts with linear (Kalman) filtering and progresses to non-linear filtering for semimartingale state and observation processes. The course also includes numerical methods like Markov chain approximations, Galerkin approximations, and particle filtering, as well as applications to financial models of, e.g., interest rates or credit risk.
|Literature||Bain, A. and D.~Crisan (2009). Fundamentals of Stochastic Filtering. New York: Springer.|
Lipster, R. and A.~Shiryaev (2001). Statistics of Random Processes Volumes I and II (2nd ed.). Berlin: Springer Verlag.
|Prerequisites / Notice||Prerequisites: probability theory, basic stochastic processes, basic statistics.|
Note: The former (spring semester 2013) course title of the course unit 401-4926-13L was Filter Theory -- Theory and Applications.