Sinopsis
of volume I.- 1 Essentials of probability theory and mathematical statistics.- 2 Martingales and semimartingales: discrete time.- 3 Martingales and semimartingales: continuous time.- 4 The Wiener process, the stochastic integral over the Wiener process, and stochastic differential equations.- 5 Square integrable martingales, and structure of the functionals on a Wiener process.- 6 Nonnegative supermartingales and martingales, and the Girsanov theorem.- 7 Absolute continuity of measures corresponding to the Ito processes and processes of the diffusion type.- 8 General equations of optimal nonlinear filtering, interpolation and extrapolation of partially observable random processes.- 9 Optimal filtering, interpolation and extrapolation of Markov processes with a countable number of states.- 10 Optimal linear nonstationary filtering.
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