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...Markov chains the preceding chapter focused on decision making in face of uncertainty about one future event learning true state nature however some decisions need to take into account many events we now begin laying groundwork for this broader context particular presents probability models processes that evolve over time a probabilistic manner such are called stochastic after briefly introducing general first section remainder focuses special kind chain have prop erty probabilities involving how process will depend only present and so independent past fit description provide an especially important model is defined be indexed collection random variables xt where index t runs through given set often taken non negative integers represents measurable characteristic interest at example might represent inventory level product end week describing behavior system operating period has following structure current status can fall any m mutually exclusive cate gories states notational convenienc...