Abstract
Publisher Summary This chapter focuses on Markov chains of the probability theory. It presents a stochastic process {Xn, n = 0, 1, 2…} that takes on a finite or countable number of possible values. This set of possible values of the process is denoted by the set of nonnegative integers {0, 1, 2…}. If Xn = i, the process is said to be in state i at time n. Such a stochastic process is known as a Markov chain. The value Pij represents the probability that the process will, when in state i, next make a transition into state j. The Chapman–Kolmogorov equations provide a method for computing these n-step transition probabilities. In a finite-state Markov chain, all recurrent states are positive recurrent.
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