Markov Chains Theory and Applications
“Markov Chains Theory and Applications” by Bruno Sericola, published by Wiley on July 22, 2013, is a comprehensive exploration of Markov chains, a fundamental class of stochastic processes. This edition spans 410 pages and is presented in English. The book delves into the theoretical underpinnings of both discrete-time and continuous-time homogeneous Markov chains, highlighting their application across various fields such as operational research, computer science, and communication networks.
Readers will find a detailed examination of key concepts including the explosion phenomenon, Kolmogorov equations, and convergence to equilibrium. The author also discusses passage time distributions and their relevance to birth-and-death processes. Additionally, the text offers an in-depth study of the uniformization technique through Banach algebra, which is essential for the transient analysis of queuing systems. This work serves as a valuable resource for those interested in the mathematical foundations and practical applications of Markov chains.
Official synopsis Publisher
Markov Chains: Theory and Applications
Markov chains are a fundamental class of stochastic processes. They are widely used to solve problems in a large number of domains such as operational research, computer science, communication networks and manufacturing systems. The success of Markov chains is mainly due to their simplicity of use, the large number of available theoretical results and the quality of algorithms developed for the numerical evaluation of many metrics of interest.
The author presents the theory of both discrete-time and continuous-time homogeneous Markov chains. He carefully examines the explosion phenomenon, the Kolmogorov equations, the convergence to equilibrium and the passage time distributions to a state and to a subset of states. These results are applied to birth-and-death processes. He then proposes a detailed study of the uniformization technique by means of Banach algebra. This technique is used for the transient analysis of several queuing systems.
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