| Description |
1 online resource (xx, 301 pages) : illustrations |
| Series |
Stochastic modelling and applied probability, 0172-4568 ; 28 |
|
Stochastic modelling and applied probability ; 28. 0172-4568
|
| Contents |
Fundamentals of the cycle representations of Markov processes -- 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 representations of Markov processes -- Applications of the cycle representations -- Stochastic properties in terms of circuits -- Lévy's theorem concerning positiveness of transition probabilities -- The rotational theory of Markov processes |
| Summary |
"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."--Publisher's website |
| Bibliography |
Includes bibliographical references (pages 267-296) and index |
| Notes |
Print version record |
| In |
Springer eBooks |
| Subject |
Markov processes.
|
|
Algebraic cycles.
|
|
Distribution (Probability theory)
|
|
distribution (statistics-related concept)
|
|
MATHEMATICS -- Probability & Statistics -- Stochastic Processes.
|
|
Algebraic cycles.
|
|
Markov processes.
|
|
Markov, Procesos de
|
|
Ciclos algebraicos
|
|
Algebraic cycles
|
|
Markov processes
|
| Form |
Electronic book
|
| ISBN |
9780387360812 |
|
0387360816 |
|
0387291660 |
|
9780387291666 |
|
