The Resource Cycle representations of Markov processes, Sophia L. Kalpazidou

Cycle representations of Markov processes, Sophia L. Kalpazidou

Label
Cycle representations of Markov processes
Title
Cycle representations of Markov processes
Statement of responsibility
Sophia L. Kalpazidou
Creator
Subject
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 finite-dimensional 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 cycle-decomposition 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 circle-arcs
Member of
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
  • Markov-processen
  • Cykels
  • Markov, processus de
  • Cycles algébriques
  • Algebraischer Zyklus
  • Markov-Prozess
Label
Cycle representations of Markov processes, Sophia L. Kalpazidou
Instantiates
Publication
Bibliography note
Includes bibliographical references (p. 169-190) 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 Caratheodory-Type 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
Publication
Bibliography note
Includes bibliographical references (p. 169-190) 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 Caratheodory-Type 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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