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Probability Distributions Involving Gaussian Random Variables

2007-05-24 Mathematics
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Release : 2007-05-24
Genre : Mathematics
Kind : eBook
Book Rating : 946/5 ( reviews)

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Book Synopsis Probability Distributions Involving Gaussian Random Variables by : Marvin K. Simon

Download or read book Probability Distributions Involving Gaussian Random Variables written by Marvin K. Simon. This book was released on 2007-05-24. Available in PDF, EPUB and Kindle. Book excerpt: This handbook, now available in paperback, brings together a comprehensive collection of mathematical material in one location. It also offers a variety of new results interpreted in a form that is particularly useful to engineers, scientists, and applied mathematicians. The handbook is not specific to fixed research areas, but rather it has a generic flavor that can be applied by anyone working with probabilistic and stochastic analysis and modeling. Classic results are presented in their final form without derivation or discussion, allowing for much material to be condensed into one volume.

Probability Distributions Involving Gaussian Random Variables

2008-11-01 Mathematics
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Release : 2008-11-01
Genre : Mathematics
Kind : eBook
Book Rating : 451/5 ( reviews)

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Book Synopsis Probability Distributions Involving Gaussian Random Variables by : Marvin K. Simon

Download or read book Probability Distributions Involving Gaussian Random Variables written by Marvin K. Simon. This book was released on 2008-11-01. Available in PDF, EPUB and Kindle. Book excerpt: This handbook, now available in paperback, brings together a comprehensive collection of mathematical material in one location. It also offers a variety of new results interpreted in a form that is particularly useful to engineers, scientists, and applied mathematicians. The handbook is not specific to fixed research areas, but rather it has a generic flavor that can be applied by anyone working with probabilistic and stochastic analysis and modeling. Classic results are presented in their final form without derivation or discussion, allowing for much material to be condensed into one volume.

Gaussian Random Processes

2012-12-06 Mathematics
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Release : 2012-12-06
Genre : Mathematics
Kind : eBook
Book Rating : 755/5 ( reviews)

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Book Synopsis Gaussian Random Processes by : I.A. Ibragimov

Download or read book Gaussian Random Processes written by I.A. Ibragimov. This book was released on 2012-12-06. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Gaussian Random Functions

2013-03-09 Mathematics
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Release : 2013-03-09
Genre : Mathematics
Kind : eBook
Book Rating : 745/5 ( reviews)

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Book Synopsis Gaussian Random Functions by : M.A. Lifshits

Download or read book Gaussian Random Functions written by M.A. Lifshits. This book was released on 2013-03-09. Available in PDF, EPUB and Kindle. Book excerpt: It is well known that the normal distribution is the most pleasant, one can even say, an exemplary object in the probability theory. It combines almost all conceivable nice properties that a distribution may ever have: symmetry, stability, indecomposability, a regular tail behavior, etc. Gaussian measures (the distributions of Gaussian random functions), as infinite-dimensional analogues of tht

The Normal Distribution

2012-12-06 Mathematics
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Release : 2012-12-06
Genre : Mathematics
Kind : eBook
Book Rating : 604/5 ( reviews)

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Book Synopsis The Normal Distribution by : Wlodzimierz Bryc

Download or read book The Normal Distribution written by Wlodzimierz Bryc. This book was released on 2012-12-06. Available in PDF, EPUB and Kindle. Book excerpt: This book is a concise presentation of the normal distribution on the real line and its counterparts on more abstract spaces, which we shall call the Gaussian distributions. The material is selected towards presenting characteristic properties, or characterizations, of the normal distribution. There are many such properties and there are numerous rel evant works in the literature. In this book special attention is given to characterizations generated by the so called Maxwell's Theorem of statistical mechanics, which is stated in the introduction as Theorem 0.0.1. These characterizations are of interest both intrin sically, and as techniques that are worth being aware of. The book may also serve as a good introduction to diverse analytic methods of probability theory. We use characteristic functions, tail estimates, and occasionally dive into complex analysis. In the book we also show how the characteristic properties can be used to prove important results about the Gaussian processes and the abstract Gaussian vectors. For instance, in Section 5.4 we present Fernique's beautiful proofs of the zero-one law and of the integrability of abstract Gaussian vectors. The central limit theorem is obtained via characterizations in Section 7.3.

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