| Cycle Representations of Markov Processes Contributor(s): Kalpazidou, Sophia L. (Author) |
|
 |
ISBN: 1441921214 ISBN-13: 9781441921215 Publisher: Springer OUR PRICE: $104.49 Product Type: Paperback - Other Formats Published: November 2010 |
| Additional Information |
| BISAC Categories: - Mathematics | Probability & Statistics - General |
| Dewey: 519.233 |
| Series: Stochastic Modelling and Applied Probability |
| Physical Information: 0.68" H x 6.14" W x 9.21" (1.00 lbs) 304 pages |
| Descriptions, Reviews, Etc. |
| Publisher Description: The cycle representations of Markov processes have been advanced after the publication of the ?rst edition to many directions. One main purpose of these advances was the revelation of wide-ranging interpretations of the - cle decompositions of Markov processes such as homologic decompositions, orthogonality equations, Fourier series, semigroup equations, disinteg- tions of measures, and so on, which altogether express a genuine law of real phenomena. The versatility of these interpretations is consequently motivated by the existence of algebraic-topological principles in the fundamentals of the - clerepresentationsofMarkovprocesses, whicheliberatesthestandardview on the Markovian modelling to new intuitive and constructive approaches. For instance, the ruling role of the cycles to partition the ?nite-dimensional distributions of certain Markov processes updates Poincare's spirit to - scribing randomness in terms of the discrete partitions of the dynamical phase state; also, it allows the translation of the famous Minty's painting lemma (1966) in terms of the stochastic entities. Furthermore, the methods based on the cycle formula of Markov p- cesses are often characterized by minimal descriptions on cycles, which widelyexpressaphilosophicalanalogytotheKolmogoroveanentropicc- plexity. For instance, a deeper scrutiny on the induced Markov chains into smallersubsetsofstatesprovidessimplerdescriptionsoncyclesthanonthe stochastic matrices involved in the "taboo probabilities. " Also, the rec- rencecriteriaon cyclesimprovepreviousconditionsbased on thestochastic matrices, and provide plenty of examples. |