Statistics of Random Processes I: General Theory
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
New York, NY
Springer New York
1977
|
| Schriftenreihe: | Applications of Mathematics
5 |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | 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 |
| Beschreibung: | 1 Online-Ressource (X, 395 p) |
| ISBN: | 9781475716658 9781475716672 |
| ISSN: | 0172-4568 |
| DOI: | 10.1007/978-1-4757-1665-8 |
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| 245 | 1 | 0 | |a Statistics of Random Processes I |b General Theory |c by R. S. Liptser, A. N. Shiryayev |
| 264 | 1 | |a New York, NY |b Springer New York |c 1977 | |
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| 490 | 0 | |a Applications of Mathematics |v 5 |x 0172-4568 | |
| 500 | |a 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 | ||
| 650 | 4 | |a Mathematics | |
| 650 | 4 | |a Distribution (Probability theory) | |
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| 650 | 4 | |a Mathematik | |
| 650 | 4 | |a Statistik | |
| 700 | 1 | |a Shiryayev, A. N. |e Sonstige |4 oth | |
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Datensatz im Suchindex
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| author | Liptser, R. S. |
| author_facet | Liptser, R. S. |
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| building | Verbundindex |
| bvnumber | BV042421270 |
| classification_tum | MAT 000 |
| collection | ZDB-2-SMA ZDB-2-BAE |
| ctrlnum | (OCoLC)863978686 (DE-599)BVBBV042421270 |
| dewey-full | 519.2 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 519 - Probabilities and applied mathematics |
| dewey-raw | 519.2 |
| dewey-search | 519.2 |
| dewey-sort | 3519.2 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| doi_str_mv | 10.1007/978-1-4757-1665-8 |
| format | Electronic eBook |
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| id | DE-604.BV042421270 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T01:21:08Z |
| institution | BVB |
| isbn | 9781475716658 9781475716672 |
| issn | 0172-4568 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-027856687 |
| oclc_num | 863978686 |
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| physical | 1 Online-Ressource (X, 395 p) |
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| publishDate | 1977 |
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| publishDateSort | 1977 |
| publisher | Springer New York |
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| series2 | Applications of Mathematics |
| spelling | Liptser, R. S. Verfasser aut Statistics of Random Processes I General Theory by R. S. Liptser, A. N. Shiryayev New York, NY Springer New York 1977 1 Online-Ressource (X, 395 p) txt rdacontent c rdamedia cr rdacarrier Applications of Mathematics 5 0172-4568 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 Mathematics Distribution (Probability theory) Statistics Probability Theory and Stochastic Processes Statistics, general Mathematik Statistik Shiryayev, A. N. Sonstige oth https://doi.org/10.1007/978-1-4757-1665-8 Verlag Volltext |
| spellingShingle | Liptser, R. S. Statistics of Random Processes I General Theory Mathematics Distribution (Probability theory) Statistics Probability Theory and Stochastic Processes Statistics, general Mathematik Statistik |
| title | Statistics of Random Processes I General Theory |
| title_auth | Statistics of Random Processes I General Theory |
| title_exact_search | Statistics of Random Processes I General Theory |
| title_full | Statistics of Random Processes I General Theory by R. S. Liptser, A. N. Shiryayev |
| title_fullStr | Statistics of Random Processes I General Theory by R. S. Liptser, A. N. Shiryayev |
| title_full_unstemmed | Statistics of Random Processes I General Theory by R. S. Liptser, A. N. Shiryayev |
| title_short | Statistics of Random Processes I |
| title_sort | statistics of random processes i general theory |
| title_sub | General Theory |
| topic | Mathematics Distribution (Probability theory) Statistics Probability Theory and Stochastic Processes Statistics, general Mathematik Statistik |
| topic_facet | Mathematics Distribution (Probability theory) Statistics Probability Theory and Stochastic Processes Statistics, general Mathematik Statistik |
| url | https://doi.org/10.1007/978-1-4757-1665-8 |
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