MARKOV AND THE CREATION OF MARKOV CHAINS

We describe the life, times and legacy of Andrei Andreevich Markov (1856 -1922), and his writings on what became known as Markov chains. One focus is on his first paper [27] of 1906 on this topic, which already contains important contractivity principles embodied in the Markov Dobrushin coefficient of ergodicity, which in fact makes an explicit appearance in that paper. The contractivity principles are shown directly to underpin a number of results of the later theory. The coefficient is especially useful as a condition number in measuring the effect of perturbation of a stochastic matrix on the stationary distribution (sensitivity analysis). Some recent work in this direction is reviewed from the standpoint of the paper [53], presented at the first of the present series of conferences [63].

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