The Life and Work of A. A. Markov
The Life and Work of A. A. Markov
The Life and Work of A. A. Markov
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<strong>The</strong> Chain Gang<strong>The</strong> Concept <strong>of</strong> Chains – developments <strong>of</strong> predecessors1738 Jacob Bernoulli, “Ars Conject<strong>and</strong>i” WLLN for sequences <strong>of</strong> independentbinary r.v. X 1 , X 2 ,..., X n ,...P(X i = 1) = p <strong>and</strong> P(X i = 0) = q1837 Simeon Poisson, “Recherches sur la Probablilite des Jugements en Matiere Criminelleet en Metiere Civile” generalized Bernoulli’s theorem to includeP(X i = 1) = p i <strong>and</strong> P(X i = 0) = q i1867 Pafnuty Chebyshev, “On Mean Values” generalized WLLN to anysequence <strong>of</strong> independent r.v. with bounded second moments1898 P. A. Nekrasov, “General properties <strong>of</strong> independent events in connection with theapproximate computation <strong>of</strong> functions <strong>of</strong> very large numbers,”erroneously claims that “independence is a necessary condition for thelaw <strong>of</strong> large numbers”.1900 Andrei A. <strong>Markov</strong>, “Ischislenie veroyatnostej” further generalized WLLN tocase when variances do not exist but all moments are bounded
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