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Gaussian Random Processes (Paperback, Softcover reprint of the original 1st ed. 1978)
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Gaussian Random Processes (Paperback, Softcover reprint of the original 1st ed. 1978)
Series: Stochastic Modelling and Applied Probability, 9
Expected to ship within 10 - 15 working days
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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.
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