Titlebook: Statistics of Random Processes II; Applications Robert S. Liptser,Albert N. Shiryaev Book 2001Latest edition Springer-Verlag Berlin Heidelb

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Linear Estimation of Random Processes,se of Gaussian sequences (Lemma 14.1) for the construction of the optimal mean square linear estimate. This technique will now be used in problems of linear estimation of processes with continuous time. Here the consideration of the concept of a wide-sense Wiener process turns out to be useful.

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Parameter Estimation and Testing of Statistical Hypotheses for Diffusion-Type Processes,and .. = ..(.), ..., ..(.)) is a known vector function with the measurable deterministic components ..(.), . = 1, ..., .. The random process . = (..), ?∞ < . < ∞, is assumed stationary, .. = 0, Gaussian, with the rational spectral density . where . and the roots of the equation ..(.) = 0 lie within

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Random Point Processes: Stieltjes Stochastic Integrals,s, to a certain extent, to those of a Wiener process. Chapters 18 and 19 will deal with the case of an observable process that is a point process whose trajectories are pure jump functions (a Poisson process with constant or variable intensity is a typical example).

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Asymptotically Optimal Filtering, the conditionally Gaussian filter (Chapters 11 and 13), the Wonham type filter and the Kushner-Zakai filter (Chapter 8), were presented. However in applications, realistic filtering models have a more complicated structure than those to which the filters mentioned above are immediately applicable.