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Stochastic Modelling and Applied Probability #28: Cycle Representations of Markov Processes

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Stochastic Modelling and Applied Probability #28: Cycle Representations of Markov Processes Cover

 

Synopses & Reviews

Publisher Comments:

This book is a prototype providing new insight into Markovian dependence via the cycle decompositions. It presents a 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 Markov process. An important application of this approach is the insight it provides to electrical networks and the duality principle of networks. In particular, it provides an entirely new approach to infinite electrical networks and their applications in topics as diverse as random walks, the classification of Riemann surfaces, and to operator theory. The second edition of this book adds new advances to many directions, which reveal wide-ranging interpretations of the cycle representations like homologic decompositions, orthogonality equations, Fourier series, semigroup equations, and disintegration of measures. The versatility of these interpretations is consequently motivated by the existence of algebraic-topological principles in the fundamentals of the cycle representations. This book contains chapter summaries as well as a number of detailed illustrations. Review of the earlier edition: "This is a very useful monograph which avoids ready ways and opens new research perspectives. It will certainly stimulate further work, especially on the interplay of algebraic and geometrical aspects of Markovian dependence and its generalizations." Math Reviews.

Table of Contents

Preface.- Acknowledgements.- Preface to the Second Edition.- Directed Circuits.- Genesis of Markov Chains by Circuits: The Circuit Chains.- Cycle Representations of Recurrent Denumerable Markov Chains.- Circuit Representations of Finite Recurrent Markov Chains.- Continuous Parameter Circuit Processes with Finite State Space.- Spectral Theory of Circuit Processes.- Higher Order Circuit Processes.- Cycloid Markov Processes.- Markov Processes on Banach Spaces on Cycles.- The Cycle Measures.- Wide-Ranging Interpretations of the Cycle Processes.- Stochastic Properties in Terms of Circuits.- Levy's Theorem Concerning Positiveness of Transition Probabilities.- The Rotational Theory of Markov Processes.

Product Details

ISBN:
9780387291666
Author:
Kalpazidou, Sophia L.
Publisher:
Springer
Author:
Kalpazidou, S. L.
Location:
New York, NY
Subject:
Markov processes
Subject:
Algebraic cycles.
Subject:
Probability & Statistics - General
Subject:
Statistics
Subject:
Probability Theory and Stochastic Processes <P>This book provides new insight into Markovian dependence via the cycle decompositions. It presents a systematic account of a class of stochastic processes known as cycle (or circuit) processes - so-called bec
Subject:
Mathematics | Probability and Statistics
Subject:
Probability Theory and Stochastic Processes
Subject:
Mathematics
Subject:
B
Subject:
mathematics and statistics
Subject:
Distribution (Probability theory)
Copyright:
Edition Number:
2
Edition Description:
2nd ed. 2006
Series:
Stochastic Modelling and Applied Probability
Series Volume:
28
Publication Date:
20060524
Binding:
HARDCOVER
Language:
English
Illustrations:
Y
Pages:
324
Dimensions:
235 x 155 mm 1390 gr

Related Subjects

Children's » General
Science and Mathematics » Mathematics » Applied
Science and Mathematics » Mathematics » General
Science and Mathematics » Mathematics » Probability and Statistics » General
Science and Mathematics » Mathematics » Probability and Statistics » Probability Theory
Science and Mathematics » Mathematics » Probability and Statistics » Statistics
Science and Mathematics » Physics » Classical Mechanics

Stochastic Modelling and Applied Probability #28: Cycle Representations of Markov Processes New Hardcover
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