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Stochastic processes --- Markov processes --- 519.217 --- Markov processes. --- Markov chains --- Markov chains. --- 519.217 Markov processes

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STOCHASTIC PROCESSES[STATIONARY-] --- MARKOV CHAINS --- RENEWAL THEORY[PROBABILITY] --- Stochastic processes --- COUNTING PROCESSES --- POISSON PROCESSES --- Probabilities

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Discrete mathematics --- Graph theory --- Graph theory. --- Circuits --- Markov chains --- Network analysis theory --- Network flows --- Network synthesis --- Paths --- Trees mathematics

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This Springer brief addresses the challenges encountered in the study of the optimization of time-nonhomogeneous Markov chains. It develops new insights and new methodologies for systems in which concepts such as stationarity, ergodicity, periodicity and connectivity do not apply. This brief introduces the novel concept of confluencity and applies a relative optimization approach. It develops a comprehensive theory for optimization of the long-run average of time-nonhomogeneous Markov chains. The book shows that confluencity is the most fundamental concept in optimization, and that relative optimization is more suitable for treating the systems under consideration than standard ideas of dynamic programming. Using confluencity and relative optimization, the author classifies states as confluent or branching and shows how the under-selectivity issue of the long-run average can be easily addressed, multi-class optimization implemented, and Nth biases and Blackwell optimality conditions derived. These results are presented in a book for the first time and so may enhance the understanding of optimization and motivate new research ideas in the area.

Markov processes. --- Analysis, Markov --- Chains, Markov --- Markoff processes --- Markov analysis --- Markov chains --- Markov models --- Models, Markov --- Processes, Markov --- Stochastic processes

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Stochastic processes --- Probability --- Statistics --- Markov processes --- Markov, Processus de --- 519.217.2 --- 519.217 --- #SBIB:303H521 --- 519.2 --- Analysis, Markov --- Chains, Markov --- Markoff processes --- Markov analysis --- Markov chains --- Markov models --- Models, Markov --- Processes, Markov --- Markov chains. Processes with finite or countable set of states --- Methoden sociale wetenschappen: waarschijnlijkheid --- Probability. Mathematical statistics --- Markov processes. --- 519.2 Probability. Mathematical statistics --- 519.217 Markov processes --- 519.217.2 Markov chains. Processes with finite or countable set of states --- Probability.