Author | Liptser, R. S. author |
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Title | Statistics of Random Processes I [electronic resource] : General Theory / by R. S. Liptser, A. N. Shiryayev |
Imprint | New York, NY : Springer New York : Imprint: Springer, 1977 |
Connect to | http://dx.doi.org/10.1007/978-1-4757-1665-8 |
Descript | X, 395 p. online resource |
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