Statistics of Random Processes I: General Theory

✍ Scribed by R. S. Liptser, A. N. Shiryayev (auth.)

Publisher: Springer New York
Year: 1977
Tongue: English
Leaves: 405
Series: Applications of Mathematics 5
Category: Library

No coin nor oath required. For personal study only.

✦ Table of Contents

Front Matter....Pages i-x
Introduction....Pages 1-10
Essentials of probability theory and mathematical statistics....Pages 11-36
Martingales and semimartingales: discrete time....Pages 37-54
Martingales and semimartingales: continuous time....Pages 55-81
The Wiener process, the stochastic integral over the Wiener process, and stochastic differential equations....Pages 82-151
Square integrable martingales, and structure of the functionals on a Wiener process....Pages 152-206
Nonnegative supermartingales and martingales, and the Girsanov theorem....Pages 207-235
Absolute continuity of measures corresponding to the Ito processes and processes of the diffusion type....Pages 236-296
General equations of optimal nonlinear filtering, interpolation and extrapolation of partially observable random processes....Pages 297-328
Optimal filtering, interpolation and extrapolation of Markov processes with a countable number of states....Pages 329-350
Optimal linear nonstationary filtering....Pages 351-380
Back Matter....Pages 381-395

✦ Subjects

Probability Theory and Stochastic Processes; Statistics, general

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