Resolving Markov Chains onto Bernoulli Shifts via Positive Polynomials PDF Download
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Author: Brian Marcus
Publisher: American Mathematical Soc.
ISBN: 0821826468
Category : Biography & Autobiography
Languages : en
Pages : 114
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Book Description
The two parts of this monograph contain two separate but related papers. The longer paper in Part A obtains necessary and sufficient conditions for several types of codings of Markov chains onto Bernoulli shifts. It proceeds by replacing the defining stochastic matrix of each Markov chain by a matrix whose entries are polynomials with positive coefficients in several variables; a Bernoulli shift is represented by a single polynomial with positive coefficients, $p$. This transforms jointly topological and measure-theoretic coding problems into combinatorial ones. In solving the combinatorial problems in Part A, the work states and makes use of facts from Part B concerning $p DEGREESn$ and its coefficients. Part B contains the shorter paper on $p DEGREESn$ and its coefficients, and is independ
Author: Brian Marcus
Publisher: American Mathematical Soc.
ISBN: 0821826468
Category : Biography & Autobiography
Languages : en
Pages : 114
Get Book Here
Book Description
The two parts of this monograph contain two separate but related papers. The longer paper in Part A obtains necessary and sufficient conditions for several types of codings of Markov chains onto Bernoulli shifts. It proceeds by replacing the defining stochastic matrix of each Markov chain by a matrix whose entries are polynomials with positive coefficients in several variables; a Bernoulli shift is represented by a single polynomial with positive coefficients, $p$. This transforms jointly topological and measure-theoretic coding problems into combinatorial ones. In solving the combinatorial problems in Part A, the work states and makes use of facts from Part B concerning $p DEGREESn$ and its coefficients. Part B contains the shorter paper on $p DEGREESn$ and its coefficients, and is independ
Author: L. Rodman
Publisher: American Mathematical Soc.
ISBN: 0821829963
Category : Mathematics
Languages : en
Pages : 87
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Book Description
In this work, versions of an abstract scheme are developed, which are designed to provide a framework for solving a variety of extension problems. The abstract scheme is commonly known as the band method. The main feature of the new versions is that they express directly the conditions for existence of positive band extensions in terms of abstract factorizations (with certain additional properties). The results prove, amongst other things, that the band extension is continuous in an appropriate sense.
Author: Georgios K. Alexopoulos
Publisher: American Mathematical Soc.
ISBN: 0821827642
Category : Mathematics
Languages : en
Pages : 119
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Book Description
This work is intended for graduate students and research mathematicians interested in topological groups, Lie groups, and harmonic analysis.
Author: Douglas Bowman
Publisher: American Mathematical Soc.
ISBN: 082182774X
Category : Mathematics
Languages : en
Pages : 73
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Book Description
The author explores ramifications and extensions of a $q$-difference operator method first used by L.J. Rogers for deriving relationships between special functions involving certain fundamental $q$-symmetric polynomials. In special cases these symmetric polynomials reduce to well-known classes of orthogonal polynomials. A number of basic properties of these polynomials follow from this approach. This leads naturally to the evaluation of the Askey-Wilson integral and generalizations. Expansions of certain generalized basic hypergeometric functions in terms of the symmetric polynomials are also found. This provides a quick route to understanding the group structure generated by iterating the two-term transformations of these functions. Some infrastructure is also laid for more general investigations in the future
Author: Lisa Carbone
Publisher: American Mathematical Soc.
ISBN: 0821827219
Category : Mathematics
Languages : en
Pages : 146
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Book Description
This title provides a comprehensive examination of non-uniform lattices on uniform trees. Topics include graphs of groups, tree actions and edge-indexed graphs; $Aut(x)$ and its discrete subgroups; existence of tree lattices; non-uniform coverings of indexed graphs with an arithmetic bridge; non-uniform coverings of indexed graphs with a separating edge; non-uniform coverings of indexed graphs with a ramified loop; eliminating multiple edges; existence of arithmetic bridges. This book is intended for graduate students and research mathematicians interested in group theory and generalizations.
Author: Richard Durrett
Publisher: American Mathematical Soc.
ISBN: 0821827685
Category : Mathematics
Languages : en
Pages : 133
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Book Description
In (1994) Durrett and Levin proposed that the equilibrium behavior of stochastic spatial models could be determined from properties of the solution of the mean field ordinary differential equation (ODE) that is obtained by pretending that all sites are always independent. Here we prove a general result in support of that picture. We give a condition on an ordinary differential equation which implies that densities stay bounded away from 0 in the associated reaction-diffusion equation, and that coexistence occurs in the stochastic spatial model with fast stirring. Then using biologists' notion of invadability as a guide, we show how this condition can be checked in a wide variety of examples that involve two or three species: epidemics, diploid genetics models, predator-prey systems, and various competition models.
Author: Jesús Bastero
Publisher: American Mathematical Soc.
ISBN: 0821827340
Category : Mathematics
Languages : en
Pages : 94
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Book Description
Introduction Calderon weights Applications to real interpolation: reiteration and extrapolation Other classes of weights Extrapolation of weighted norm inequalities via extrapolation theory Applications to function spaces Commutators defined by the K-method Generalized commutators The quasi Banach case Applications to harmonic analysis BMO type spaces associated to Calderon weights Atomic decompositions and duality References.
Author: Michael Grosser
Publisher: American Mathematical Soc.
ISBN: 0821827294
Category : Mathematics
Languages : en
Pages : 113
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Book Description
In part 1 of this title the authors construct a diffeomorphism invariant (Colombeau-type) differential algebra canonically containing the space of distributions in the sense of L. Schwartz. Employing differential calculus in infinite dimensional (convenient) vector spaces, previous attempts in this direction are unified and completed. Several classification results are achieved and applications to nonlinear differential equations involving singularities are given.
Author: Yasuro Gon
Publisher: American Mathematical Soc.
ISBN: 0821827634
Category : Mathematics
Languages : en
Pages : 130
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Book Description
Obtains an explicit formula for generalized Whittaker functions and multiplicity one theorem for all discrete series representations of $SU(2,2)$.
Author: Heng Sun
Publisher: American Mathematical Soc.
ISBN: 0821827758
Category : Mathematics
Languages : en
Pages : 79
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Book Description
Let $F$ be a number field and ${\bf A}$ the ring of adeles over $F$. Suppose $\overline{G({\bf A})}$ is a metaplectic cover of $G({\bf A})=GL(r, {\bf A})$ which is given by the $n$-th Hilbert symbol on ${\bf A}$
