The Life and Work of A. A. Markov

More documents

Recommendations

Info

Chains, WLLN, and the CLTWLLN (1906)• Markov used a 2-state MC (0 and 1) and Chebyshev’s inequalityto prove that the WLLN applies to his r.v. with Markovdependence.• concluded that “the independence of variables does not produce the necessarycondition for the validity of the law of large numbers.”CLT (1907-1911)• used the method of moments from Chebyshev to prove that theCLT can be applied to his chains.
Markov’s Extensions to his Chains1910 studies simple 2-state nonhomogeneous chain, “Investigation of thegeneral case of trials connected in a chain”1911 studies complex homogeneous chains with dependence onpreceding two states, can’t establish ergodic property1913 publishes 3 rd edition of his book, “The Calculus of Probabilities”– adds work from 1906-1913 on chains– “Let us finish the article and the whole book with a good example of thedependent trials, which approximately can be regarded as a simple chain.”
Page 1 and 2: TheLifeandWorkofA.A.MarkovAmy Langv
Page 5 and 6: Roots of Prob. theory begin at Acad
Page 7 and 8: Chebyshev as a teacher• Chebyshev
Page 9: Markov’s Academic Timeline (cont.
Page 14 and 15: Markov the Teacher• interested in
Page 16 and 17: Markov the Political Activist• Gr
Page 18: Markov’s Personal Timeline• 185
Page 23 and 24: PrehistoryUrn problems (Laplace, D.
Page 26 and 27: The Missing Link• Markov wanted t
Page 28: The Missing LinkThe Concept of Chai
Page 31: Markov’s Theorems for Chains1906c
Page 35 and 36: A.S.Pushkin. Eugeny Onegin (1-3 cha
Page 37: Calculations for “Eugeny Onegin
Page 42 and 43: Best OR/MS in past millennium(INFOR
Page 48 and 49: REFERENCES1. J. Bernoulli, Ars Conj

The Life and Work of A. A. Markov

Create successful ePaper yourself

Delete template?

Save as template?