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Titlebook: Statistics of Random Processes I; General Theory R. S. Liptser,A. N. Shiryayev Book 19771st edition Springer-Verlag New York 1977 Markov pr

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Absolute continuity of measures corresponding to the Ito processes and processes of the diffusion tLet (0, ., P) be a complete probability space, let F = (. .), t ≥ 0, be a nondecreasing family of sub-σ-algebras, and let . = (. ., . .), t ≥ 0, be a Wiener process.
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Optimal filtering, interpolation and extrapolation of Markov processes with a countable number of sThe present chapter will be concerned with a pair of random processes . where the unobservable component . is a Markov process with a finite or countable number of states, and the observable process permits the stochastic differential . where .. is a Wiener process.
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Optimal linear nonstationary filtering,On the probability space (Ω,.,.) with a distinguished family of the .-algebras (..),. ≤ ., we shall consider the two-dimensional Gaussian random process (..,..),0 ≤ . ≤ .,satisfying the stochastic differential equations . where .. =(..(.)..)and .. =(..(.)..) are two independent Wiener processes and ..,.., are ..-measurable.
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Book 19771st editionnal expectation M(lJ/lff;) can be computed by Bayes‘ formula. However, even in many rather simple cases, equations obtained by Bayes‘ formula are too cumbersome, and present difficulties in their practical application as well as in the investigation of the structure and properties of the solution.
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des philosophers (e.g., philosophers of mind, philosophers of biology, and metaethicists), as well as practicing scientists, such as biologists or psychologists whose interests relate to biological explanations of behavior.  .978-94-007-3732-7978-94-007-1951-4Series ISSN 0068-0346 Series E-ISSN 2214-7942
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R. S. Liptser,A. N. Shiryayevdes philosophers (e.g., philosophers of mind, philosophers of biology, and metaethicists), as well as practicing scientists, such as biologists or psychologists whose interests relate to biological explanations of behavior.  .978-94-007-3732-7978-94-007-1951-4Series ISSN 0068-0346 Series E-ISSN 2214-7942
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