Gaussian Random Processes

Beschreibung

Neuware -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.Springer Verlag GmbH, Tiergartenstr. 17, 69121 Heidelberg 292 pp. Englisch.

Bestandsnummer des Verkäufers 9781461262770

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Bibliografische Details

Titel

Gaussian Random Processes

Verlag

Springer New York, Springer New York Nov 2011

Veröffentlichungsdatum

2011

Sprache

Englisch

ISBN-10

1461262771

ISBN-13

9781461262770

Bindung

Taschenbuch

Zustand

Neu

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