Beschreibung
Inhaltsverzeichnis
Essentials of probability theory and mathematical statistics.- Martingales and related processes.- Martingales and supermartingales: continuous time.- The Wiener process, the stochastic integral over the Wiener process, and stochastic differential equations.- Square integrable martingales, and structure of the functionals on a Wiener process.- Nonnegative supermartingales and martingales, and the Girsanovs theorem.- Absolute continuity of measures corresponding to the Ito processes and processes of diffusion type.- General equations of optimal nonlinear filtering, interpolation and extrapolation of partially observable random processes.- Optimal filtering, interpolation and extrapolation of Markov processes with countable number of states.- Optimal linear nonstationary filtering.