STATISTICS OF RANDOM PROCESSES I: General Theory.

Lipster, R. S. ; A. N. Shiryayev.

ISBN 10: 0387902260 / ISBN 13: 9780387902265

Editore: Springer-Verlag,, 1977

Hardback first printing of the 1977 edition; revised and expanded translation of the authors' Statistika Sluchainyk Protsessov, published in 1974. VOLUME I ONLY. Light cover soil, cover wear; previous owner's name in ink on front endpaper. Contents clean, tight. No DJ. Translated into English by A. B. Aries. Not library discard. ; Codice articolo 46082

Riassunto:

A considerable number of problems in the statistics of random processes are formulated within the following scheme. On a certain probability space (Q, ff, P) a partially observable random process (lJ,~) = (lJ ~/), t :;::-: 0, is given with only the second component n ~ = (~/), t:;::-: 0, observed. At any time t it is required, based on ~h = g., ° s sst}, to estimate the unobservable state lJ/. This problem of estimating (in other words, the filtering problem) 0/ from ~h will be discussed in this book. It is well known that if M(lJ;) < 00, then the optimal mean square esti­ mate of lJ/ from ~h is the a posteriori mean m/ = M(lJ/1 ff~), where ff~ = CT{ w: ~., sst} is the CT-algebra generated by ~h. Therefore, the solution of the problem of optimal (in the mean square sense) filtering is reduced to finding the conditional (mathematical) expectation m/ = M(lJ/lffa. In principle, the conditional 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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Titolo: STATISTICS OF RANDOM PROCESSES I: General ...
Casa editrice: Springer-Verlag,
Data di pubblicazione: 1977
Legatura: Hardcover
Condizione: G+
Condizione sovraccoperta: No Dust Jacket
Edizione: prima edizione