9781441921215 - Cycle Representations of Markov Processes (Stochastic Modelling and Applied Probability, Band 28) von Kalpazidou, Sophia L. L. (2 Ergebnisse)

Paperback. Zustand: Brand New. 2nd ed. edition. 301 pages. 9.00x6.00x0.73 inches. In Stock.

Taschenbuch. Zustand: Neu. Druck auf Anfrage Neuware - Printed after ordering - 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,whicheliberatesthestandardvi ew 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.