Titlebook: Markov Chains and Stochastic Stability; Sean P. Meyn,Richard L. Tweedie Book 1993 Springer-Verlag London Limited 1993 Drift.Markov.Markov

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https://doi.org/10.1007/978-1-4471-3267-7Drift; Markov; Markov chain; Markov model; Symbol; Transit; calculus; communication; control; control enginee

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HeuristicsThis book is about Markovian models, and particularly about the structure and stability of such models. We develop a theoretical basis by studying Markov chains in very general contexts; and we develop, as systematically as we can, the applications of this theory to applied models in systems engineering, in operations research, and in time series.

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Markov ModelsThe results presented in this book have been written in the desire that practitioners will use them. We have tried therefore to illustrate the use of the theory in a systematic and accessible way, and so this book concentrates not only on the theory of general space Markov chains, but on the application of that theory in considerable detail.

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Transition ProbabilitiesAs with all stochastic processes, there are two directions from which to approach the formal definition of a Markov chain.

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Invariance and TightnessIn one of our heuristic descriptions of stability, in Section 1.3, we outlined a picture of a chain settling down to a stable regime independent of its initial starting point: we will show in Part III that positive Harris chains do precisely this, and one role of π is to describe the final stochastic regime of the chain, as we have seen.