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The Resource Cycle representations of Markov processes, Sophia L. Kalpazidou
Cycle representations of Markov processes, Sophia L. Kalpazidou
Resource Information
The item Cycle representations of Markov processes, Sophia L. Kalpazidou represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in Boston University Libraries.This item is available to borrow from all library branches.
Resource Information
The item Cycle representations of Markov processes, Sophia L. Kalpazidou represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in Boston University Libraries.
This item is available to borrow from all library branches.
 Summary

 This book presents an original and systematic account of a class of stochastic processes known as cycle (or circuit) processes, so called because they may be defined by directed cycles. These processes have special and important properties through the interaction between the geometric properties of the trajectories and the algebraic characterization of the finitedimensional distributions. An important application of this approach is the new insight it provides into Markovian dependence and electrical networks. In particular, it provides an entirely new approach to Markov processes and infinite electrical networks, and their applications in topics as diverse as random walks, ergodic theory, dynamical systems, potential theory, theory of matrices, algebraic topology, complexity theory, the classification of Riemann surfaces, and operator theory
 The author surveys the three principal developments in cycle theory: the cycledecomposition formula and its relation to the Markov process; entropy production and how it may be used to measure how far a process is from being reversible; and how a finite recurrent stochastic matrix may be defined by a rotation of the circle and a partition whose elements consist of finite unions of circlearcs
 Language
 eng
 Extent
 xv, 194 pages
 Contents

 Directed Circuits. Definition of Directed Circuits. The Passage Functions. Cycle Generating Equations
 Genesis of Markov Chains by Circuits: The Circuit Chains. Finite Markov Chains Defined by Weighted Circuits. Denumerable Markov Chains Generated by Circuits
 Cycle Representations of Recurrent Denumerable Markov Chains. The Derived Chain of Qians. The Circulation Distribution of a Markov Chain. A Probabilistic Cycle Decomposition for Recurrent Markov Chains. Weak Convergence of Sequences of Circuit Chains: A Deterministic Approach. Weak Convergence of Sequences of Circuit Chains: A Probabilistic Approach
 Circuit Representations of Finite Recurrent Markov Chains. Circuit Representations by Probabilistic Algorithms. Circuit Representations by Nonrandomized Algorithms. The CaratheodoryType Circuit Representations. The Betti Number of a Markov Chain. A Refined Cycle Decomposition of Finite Stochastic Matrices: A Homologic Approach. The Dimensions of Caratheodory and Betti
 Isbn
 9783540943631
 Label
 Cycle representations of Markov processes
 Title
 Cycle representations of Markov processes
 Statement of responsibility
 Sophia L. Kalpazidou
 Language
 eng
 Summary

 This book presents an original and systematic account of a class of stochastic processes known as cycle (or circuit) processes, so called because they may be defined by directed cycles. These processes have special and important properties through the interaction between the geometric properties of the trajectories and the algebraic characterization of the finitedimensional distributions. An important application of this approach is the new insight it provides into Markovian dependence and electrical networks. In particular, it provides an entirely new approach to Markov processes and infinite electrical networks, and their applications in topics as diverse as random walks, ergodic theory, dynamical systems, potential theory, theory of matrices, algebraic topology, complexity theory, the classification of Riemann surfaces, and operator theory
 The author surveys the three principal developments in cycle theory: the cycledecomposition formula and its relation to the Markov process; entropy production and how it may be used to measure how far a process is from being reversible; and how a finite recurrent stochastic matrix may be defined by a rotation of the circle and a partition whose elements consist of finite unions of circlearcs
 Cataloging source
 DLC
 http://library.link/vocab/creatorName
 Kalpazidou, Sophia L
 Illustrations
 illustrations
 Index
 index present
 LC call number
 QA274.7
 LC item number
 .K354 1995
 Literary form
 non fiction
 Nature of contents
 bibliography
 http://library.link/vocab/subjectName

 Markov processes
 Algebraic cycles
 Algebraic cycles
 Markov processes
 Markovprocessen
 Cykels
 Markov, processus de
 Cycles algébriques
 Algebraischer Zyklus
 MarkovProzess
 Label
 Cycle representations of Markov processes, Sophia L. Kalpazidou
 Bibliography note
 Includes bibliographical references (p. 169190) and index
 Carrier category
 volume
 Carrier category code
 nc
 Carrier MARC source
 rdacarrier
 Content category
 text
 Content type code
 txt
 Content type MARC source
 rdacontent
 Contents
 Directed Circuits. Definition of Directed Circuits. The Passage Functions. Cycle Generating Equations  Genesis of Markov Chains by Circuits: The Circuit Chains. Finite Markov Chains Defined by Weighted Circuits. Denumerable Markov Chains Generated by Circuits  Cycle Representations of Recurrent Denumerable Markov Chains. The Derived Chain of Qians. The Circulation Distribution of a Markov Chain. A Probabilistic Cycle Decomposition for Recurrent Markov Chains. Weak Convergence of Sequences of Circuit Chains: A Deterministic Approach. Weak Convergence of Sequences of Circuit Chains: A Probabilistic Approach  Circuit Representations of Finite Recurrent Markov Chains. Circuit Representations by Probabilistic Algorithms. Circuit Representations by Nonrandomized Algorithms. The CaratheodoryType Circuit Representations. The Betti Number of a Markov Chain. A Refined Cycle Decomposition of Finite Stochastic Matrices: A Homologic Approach. The Dimensions of Caratheodory and Betti
 Dimensions
 25 cm.
 Extent
 xv, 194 pages
 Isbn
 9783540943631
 Lccn
 94028223
 Media category
 unmediated
 Media MARC source
 rdamedia
 Media type code
 n
 Other physical details
 illustrations
 System control number

 (OCoLC)30734812
 (OCoLC)ocm30734812
 Label
 Cycle representations of Markov processes, Sophia L. Kalpazidou
 Bibliography note
 Includes bibliographical references (p. 169190) and index
 Carrier category
 volume
 Carrier category code
 nc
 Carrier MARC source
 rdacarrier
 Content category
 text
 Content type code
 txt
 Content type MARC source
 rdacontent
 Contents
 Directed Circuits. Definition of Directed Circuits. The Passage Functions. Cycle Generating Equations  Genesis of Markov Chains by Circuits: The Circuit Chains. Finite Markov Chains Defined by Weighted Circuits. Denumerable Markov Chains Generated by Circuits  Cycle Representations of Recurrent Denumerable Markov Chains. The Derived Chain of Qians. The Circulation Distribution of a Markov Chain. A Probabilistic Cycle Decomposition for Recurrent Markov Chains. Weak Convergence of Sequences of Circuit Chains: A Deterministic Approach. Weak Convergence of Sequences of Circuit Chains: A Probabilistic Approach  Circuit Representations of Finite Recurrent Markov Chains. Circuit Representations by Probabilistic Algorithms. Circuit Representations by Nonrandomized Algorithms. The CaratheodoryType Circuit Representations. The Betti Number of a Markov Chain. A Refined Cycle Decomposition of Finite Stochastic Matrices: A Homologic Approach. The Dimensions of Caratheodory and Betti
 Dimensions
 25 cm.
 Extent
 xv, 194 pages
 Isbn
 9783540943631
 Lccn
 94028223
 Media category
 unmediated
 Media MARC source
 rdamedia
 Media type code
 n
 Other physical details
 illustrations
 System control number

 (OCoLC)30734812
 (OCoLC)ocm30734812
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