Statistics of Random Processes: Vol. I - General Theory; Vol. II - Applications

Liptser, R. S.; Shiriaev, A. N.

ISBN 10: 0387902260 / ISBN 13: 9780387902265

Editore: Springer-Verlag, 1977

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Springer-Verlag, 1977. Two-Volume Set; covers lightly rubbed/bumped/soiled, spines/front board of Vol. II sunned; edges very lightly sunned/soiled; faint pencil erasuers at ffeps; binding tight; cover, edges and interior intact and clean, except where noted. hardcover. Good.

Codice articolo 603580

Dati bibliografici

• Titolo: Statistics of Random Processes: Vol. I - General Theory; Vol. II - Applications
• Editore: Springer-Verlag
• Data di pubblicazione: 1977
• Lingua: Inglese
• ISBN 10: 0387902260
• ISBN 13: 9780387902265
• Rilegatura: Rilegato
• Condizione: Good
• Cataloghi dei venditori:
  • New Additions
  • Mathematics
  • EMath

Descrizione articolo

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.