Limit Theorems for Functionals of Ergodic Markov Chains with General State Space PDF Download
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Author: Xia Chen
Publisher: American Mathematical Soc.
ISBN: 082181060X
Category : Mathematics
Languages : en
Pages : 225
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Book Description
This book is intended for graduate students and research mathematicians working probability theory and statistics.
Author: Xia Chen
Publisher: American Mathematical Soc.
ISBN: 082181060X
Category : Mathematics
Languages : en
Pages : 225
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Book Description
This book is intended for graduate students and research mathematicians working probability theory and statistics.
Author: Hubert Hennion
Publisher: Springer Science & Business Media
ISBN: 3540424156
Category : Mathematics
Languages : en
Pages : 150
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Book Description
This book shows how techniques from the perturbation theory of operators, applied to a quasi-compact positive kernel, may be used to obtain limit theorems for Markov chains or to describe stochastic properties of dynamical systems. A general framework for this method is given and then applied to treat several specific cases. An essential element of this work is the description of the peripheral spectra of a quasi-compact Markov kernel and of its Fourier-Laplace perturbations. This is first done in the ergodic but non-mixing case. This work is extended by the second author to the non-ergodic case. The only prerequisites for this book are a knowledge of the basic techniques of probability theory and of notions of elementary functional analysis.
Author: Florence Merlevède
Publisher: Oxford University Press
ISBN: 0192561863
Category : Mathematics
Languages : en
Pages : 495
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Book Description
Functional Gaussian Approximation for Dependent Structures develops and analyses mathematical models for phenomena that evolve in time and influence each another. It provides a better understanding of the structure and asymptotic behaviour of stochastic processes. Two approaches are taken. Firstly, the authors present tools for dealing with the dependent structures used to obtain normal approximations. Secondly, they apply normal approximations to various examples. The main tools consist of inequalities for dependent sequences of random variables, leading to limit theorems, including the functional central limit theorem and functional moderate deviation principle. The results point out large classes of dependent random variables which satisfy invariance principles, making possible the statistical study of data coming from stochastic processes both with short and long memory. The dependence structures considered throughout the book include the traditional mixing structures, martingale-like structures, and weakly negatively dependent structures, which link the notion of mixing to the notions of association and negative dependence. Several applications are carefully selected to exhibit the importance of the theoretical results. They include random walks in random scenery and determinantal processes. In addition, due to their importance in analysing new data in economics, linear processes with dependent innovations will also be considered and analysed.
Author: Jean-Luc Joly
Publisher: American Mathematical Soc.
ISBN: 0821820419
Category : Mathematics
Languages : en
Pages : 87
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Book Description
This book is intended for graduate students and research mathematicians interested in partial differential equations.
Author: Henning Krause
Publisher: American Mathematical Soc.
ISBN: 0821826182
Category : Mathematics
Languages : en
Pages : 143
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Book Description
These notes present an introduction into the spectrum of the category of modules over a ring. We discuss the general theory of pure-injective modules and concentrate on the isomorphism classes of indecomposable pure-injective modules which form the underlying set of this spectrum. The interplay between the spectrum and the category of finitely presented modules provides new insight into the geometrical and homological properties of the category of finitely presented modules. Various applications from representation theory of finite dimensional algebras are included.
Author: Harvey I. Blau
Publisher: American Mathematical Soc.
ISBN: 0821820214
Category : Mathematics
Languages : en
Pages : 109
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Book Description
Homogeneous integral table algebras of degree three with a faithful real element. The algebras of the title are classified to exact isomorphism; that is, the sets of structure constants which arise from the given basis are completely determined. Other results describe all possible extensions (pre-images), with a faithful element which is not necessarily real, of certain simple homogeneous integral table algebras of degree three. On antisymmetric homogeneous integral table algebras of degree three. This paper determines the homogeneous integral table algebras of degree three in which the given basis has a faithful element and has no nontrivial elements that are either real (symmetric) or linear, and where an additional hypothesis is satisfied. It is shown that all such bases must occur as the set of orbit sums in the complex group algebra of a finite abelian group under the action of a fixed-point-free automorphism oforder three. Homogeneous integral table algebras of degree three with no nontrivial linear elements. The algebras of the title which also have a faithful element are determined to exact isomorphism. All of the simple homogeneous integral table algebras of degree three are displayed, and the commutative association schemes in which all the nondiagonal relations have valency three and where some relation defines a connected graph on the underlying set are classified up to algebraic isomorphism.
Author: Wilhelm Stannat
Publisher: American Mathematical Soc.
ISBN: 0821813846
Category : Mathematics
Languages : en
Pages : 114
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Book Description
This text explores the theory of generalized Dirichlet Forms along with its applications for analysis and stochastics. Examples are provided.
Author: Martin Majewski
Publisher: American Mathematical Soc.
ISBN: 0821819208
Category : Mathematics
Languages : en
Pages : 175
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Book Description
The main goal of this paper is to prove the following conjecture of Baues and Lemaire: the differential graded Lie Tlgebra associated with the Sullivan model of a space is homotopy equivalent to its Quillen model. In addition we show the same for the cellular Lie algebra model which we build from the simplicial analog of the classical Adams-Hilton model. It turns out that this cellular Lie algebra model is one link in a chain of models connecting the models of Quillen and Sullivan.The key result which makes all this possible is Anick's correspondence between differential graded Lie algebras and Hopf algebras up to homotopy. In addition we show that the Quillen model is a rational homotopical equivalence, and we conclude the same for the other models using our main result. Theconstruction of the three models is given in detail. The background from homotopy theory, differential algebra, and algebra is presented in great generality.
Author: Yuri A. Abramovich
Publisher: American Mathematical Soc.
ISBN: 0821813978
Category : Mathematics
Languages : en
Pages : 178
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Book Description
This book is intended for graduate students and research mathematicians interested in operator theory, functional analysis, and vector lattices
Author: Volodymyr V. Lyubashenko
Publisher: American Mathematical Soc.
ISBN: 0821813617
Category : Mathematics
Languages : en
Pages : 197
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Book Description
This book is intended for graduate students and research mathematicians interested in associative rings and algebras.
