|
Showing 1 - 5 of
5 matches in All Departments
Stochastic Analysis for Gaussian Random Processes and Fields: With
Applications presents Hilbert space methods to study deep analytic
properties connecting probabilistic notions. In particular, it
studies Gaussian random fields using reproducing kernel Hilbert
spaces (RKHSs). The book begins with preliminary results on
covariance and associated RKHS before introducing the Gaussian
process and Gaussian random fields. The authors use chaos expansion
to define the Skorokhod integral, which generalizes the Ito
integral. They show how the Skorokhod integral is a dual operator
of Skorokhod differentiation and the divergence operator of
Malliavin. The authors also present Gaussian processes indexed by
real numbers and obtain a Kallianpur-Striebel Bayes' formula for
the filtering problem. After discussing the problem of equivalence
and singularity of Gaussian random fields (including a
generalization of the Girsanov theorem), the book concludes with
the Markov property of Gaussian random fields indexed by measures
and generalized Gaussian random fields indexed by Schwartz space.
The Markov property for generalized random fields is connected to
the Markov process generated by a Dirichlet form.
Stochastic Analysis for Gaussian Random Processes and Fields: With
Applications presents Hilbert space methods to study deep analytic
properties connecting probabilistic notions. In particular, it
studies Gaussian random fields using reproducing kernel Hilbert
spaces (RKHSs). The book begins with preliminary results on
covariance and associated RKHS before introducing the Gaussian
process and Gaussian random fields. The authors use chaos expansion
to define the Skorokhod integral, which generalizes the Ito
integral. They show how the Skorokhod integral is a dual operator
of Skorokhod differentiation and the divergence operator of
Malliavin. The authors also present Gaussian processes indexed by
real numbers and obtain a Kallianpur-Striebel Bayes' formula for
the filtering problem. After discussing the problem of equivalence
and singularity of Gaussian random fields (including a
generalization of the Girsanov theorem), the book concludes with
the Markov property of Gaussian random fields indexed by measures
and generalized Gaussian random fields indexed by Schwartz space.
The Markov property for generalized random fields is connected to
the Markov process generated by a Dirichlet form.
The first book to examine weakly stationary random fields and their
connections with invariant subspaces (an area associated with
functional analysis). It reviews current literature, presents
central issues and most important results within the area. For
advanced Ph.D. students, researchers, especially those conducting
research on Gaussian theory.
The first book to examine weakly stationary random fields and their
connections with invariant subspaces (an area associated with
functional analysis). It reviews current literature, presents
central issues and most important results within the area. For
advanced Ph.D. students, researchers, especially those conducting
research on Gaussian theory.
The purpose of this book is to present results on the subject of
weak convergence in function spaces to study invariance principles
in statistical applications to dependent random variables,
U-statistics, censor data analysis. Different techniques, formerly
available only in a broad range of literature, are for the first
time presented here in a self-contained fashion. Contents: Weak
convergence of stochastic processes Weak convergence in metric
spaces Weak convergence on C[0, 1] and D[0, ) Central limit theorem
for semi-martingales and applications Central limit theorems for
dependent random variables Empirical process Bibliography
|
|