rdf-syntax-grammar
mods:
  schema location: http://www.loc.gov/mods/v3 http://www.loc.gov/standards/mods/v3/mods-3-2.xsd
  title info:
    title: Cycle representations of Markov processes
  name:
    name part: Kalpazidou, Sophia L.
    role:
      role term: creator
  name:
    name part: SpringerLink (Online service)
  type of resource: text
  genre: bibliography
  genre: Electronic books.
  origin info:
    place:
      place term: nyu
    date issued: 1995
    issuance: monographic
  language:
    language term: eng
  physical description:
    reformatting quality: preservation
    reformatting quality: access
    form: remote
    extent: 1 online resource (xv, 194 pages) : illustrations.
  abstract: 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.
  abstract: 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.
  table of 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.
  note: Sophia L. Kalpazidou.
  note: Electronic resource.
  note: Master and use copy. Digital master created according to Benchmark for Faithful Digital Reproductions of Monographs and Serials, Version 1. Digital Library Federation, December 2002. http://purl.oclc.org/DLF/benchrepro0212 MiAaHDL
  note: digitized 2010 HathiTrust Digital Library committed to preserve pda MiAaHDL
  note: Includes bibliographical references (pages 169-190) and index.
  subject:
    topic: Markov processes
  subject:
    topic: Algebraic cycles
  subject:
    topic: Algebraic cycles
  subject:
    topic: Markov processes
  subject:
    topic: Markov-processen
  subject:
    topic: Cykels
  subject:
    topic: Markov, Processus de
  subject:
    topic: Cycles algébriques
  subject:
    topic: Algebraischer Zyklus
  subject:
    topic: Markov-Prozess
  subject:
    topic: Markov processes
  classification: QA274.7 .K354 1995
  classification: 519.2/33
  classification: 31.70
  related item:
    title info:
      title: Cycle representations of Markov processes
    name:
      name part: Kalpazidou, Sophia L.
    origin info:
      publisher: New York : Springer-Verlag, ©1995
    identifier: (DLC) 94028223
    identifier: (OCoLC)30734812
  related item:
    title info:
      title: Applications of mathematics ; 28
  identifier: 9781475739299 (electronic bk.)
  identifier: 147573929X (electronic bk.)
  identifier: 0387943633 (New York : acid-free paper)
  identifier: 9780387943633 (New York : acid-free paper)
  identifier: 3540943633 (Berlin : acid-free paper)
  identifier: 9783540943631 (Berlin : acid-free paper)
  identifier: http://proxy.library.tamu.edu/login
  record info:
    record content source: OCLCE
    record creation date: 101115
    record change date: 20260422215752.5
    record identifier: in00003510829
    language of cataloging:
      language term: eng