Gaussian Random Processes:
Saved in:
| Main Author: | |
|---|---|
| Format: | Electronic eBook |
| Language: | English |
| Published: |
New York, NY
Springer New York
1978
|
| Series: | Applications of Mathematics, Applied Probability Control Economics Information and Communication Modeling and Identification Numerical Techniques Optimization
9 |
| Subjects: | |
| Online Access: | Volltext |
| Item Description: | The book deals mainly with three problems involving Gaussian stationary processes. The first problem consists of clarifying the conditions for mutual absolute continuity (equivalence) of probability distributions of a "random process segment" and of finding effective formulas for densities of the equiva lent distributions. Our second problem is to describe the classes of spectral measures corresponding in some sense to regular stationary processes (in par ticular, satisfying the well-known "strong mixing condition") as well as to describe the subclasses associated with "mixing rate". The third problem involves estimation of an unknown mean value of a random process, this random process being stationary except for its mean, i. e. , it is the problem of "distinguishing a signal from stationary noise". Furthermore, we give here auxiliary information (on distributions in Hilbert spaces, properties of sam ple functions, theorems on functions of a complex variable, etc. ). Since 1958 many mathematicians have studied the problem of equivalence of various infinite-dimensional Gaussian distributions (detailed and sys tematic presentation of the basic results can be found, for instance, in [23]). In this book we have considered Gaussian stationary processes and arrived, we believe, at rather definite solutions. The second problem mentioned above is closely related with problems involving ergodic theory of Gaussian dynamic systems as well as prediction theory of stationary processes |
| Physical Description: | 1 Online-Ressource (X, 277 p) |
| ISBN: | 9781461262756 9781461262770 |
| ISSN: | 0172-4568 |
| DOI: | 10.1007/978-1-4612-6275-6 |
Staff View
MARC
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Record in the Search Index
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| author | Ibragimov, I. A. |
| author_facet | Ibragimov, I. A. |
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| dewey-full | 510 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 510 - Mathematics |
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| dewey-sort | 3510 |
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| discipline | Mathematik |
| doi_str_mv | 10.1007/978-1-4612-6275-6 |
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| id | DE-604.BV042420463 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T01:21:07Z |
| institution | BVB |
| isbn | 9781461262756 9781461262770 |
| issn | 0172-4568 |
| language | English |
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| series2 | Applications of Mathematics, Applied Probability Control Economics Information and Communication Modeling and Identification Numerical Techniques Optimization |
| spelling | Ibragimov, I. A. Verfasser aut Gaussian Random Processes by I. A. Ibragimov, Y. A. Rozanov New York, NY Springer New York 1978 1 Online-Ressource (X, 277 p) txt rdacontent c rdamedia cr rdacarrier Applications of Mathematics, Applied Probability Control Economics Information and Communication Modeling and Identification Numerical Techniques Optimization 9 0172-4568 The book deals mainly with three problems involving Gaussian stationary processes. The first problem consists of clarifying the conditions for mutual absolute continuity (equivalence) of probability distributions of a "random process segment" and of finding effective formulas for densities of the equiva lent distributions. Our second problem is to describe the classes of spectral measures corresponding in some sense to regular stationary processes (in par ticular, satisfying the well-known "strong mixing condition") as well as to describe the subclasses associated with "mixing rate". The third problem involves estimation of an unknown mean value of a random process, this random process being stationary except for its mean, i. e. , it is the problem of "distinguishing a signal from stationary noise". Furthermore, we give here auxiliary information (on distributions in Hilbert spaces, properties of sam ple functions, theorems on functions of a complex variable, etc. ). Since 1958 many mathematicians have studied the problem of equivalence of various infinite-dimensional Gaussian distributions (detailed and sys tematic presentation of the basic results can be found, for instance, in [23]). In this book we have considered Gaussian stationary processes and arrived, we believe, at rather definite solutions. The second problem mentioned above is closely related with problems involving ergodic theory of Gaussian dynamic systems as well as prediction theory of stationary processes Mathematics Mathematics, general Mathematik Gauß-Prozess (DE-588)4156111-9 gnd rswk-swf Stochastischer Prozess (DE-588)4057630-9 gnd rswk-swf Gauß-Prozess (DE-588)4156111-9 s 1\p DE-604 Stochastischer Prozess (DE-588)4057630-9 s 2\p DE-604 Rozanov, Y. A. Sonstige oth https://doi.org/10.1007/978-1-4612-6275-6 Verlag Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Ibragimov, I. A. Gaussian Random Processes Mathematics Mathematics, general Mathematik Gauß-Prozess (DE-588)4156111-9 gnd Stochastischer Prozess (DE-588)4057630-9 gnd |
| subject_GND | (DE-588)4156111-9 (DE-588)4057630-9 |
| title | Gaussian Random Processes |
| title_auth | Gaussian Random Processes |
| title_exact_search | Gaussian Random Processes |
| title_full | Gaussian Random Processes by I. A. Ibragimov, Y. A. Rozanov |
| title_fullStr | Gaussian Random Processes by I. A. Ibragimov, Y. A. Rozanov |
| title_full_unstemmed | Gaussian Random Processes by I. A. Ibragimov, Y. A. Rozanov |
| title_short | Gaussian Random Processes |
| title_sort | gaussian random processes |
| topic | Mathematics Mathematics, general Mathematik Gauß-Prozess (DE-588)4156111-9 gnd Stochastischer Prozess (DE-588)4057630-9 gnd |
| topic_facet | Mathematics Mathematics, general Mathematik Gauß-Prozess Stochastischer Prozess |
| url | https://doi.org/10.1007/978-1-4612-6275-6 |
| work_keys_str_mv | AT ibragimovia gaussianrandomprocesses AT rozanovya gaussianrandomprocesses |