Geodesic
On a question of limiting distribution of series in~random binary sequence
Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences, no. 4 (2012), pp. 56-71

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Limiting forms of distribution of length of the maximum series of successes in random binary sequences, formed in Bernulli–Markov's chain and in Polya's scheme which is an equivalent to local trends of a time series of strictly stationary process are investigated. More simple and added proof of theorems of the law of the big numbers for series of both types is offered. For series of the second type the effect of the cyclic bimorphism of the limiting law with degeneration on one of the phases and the convergence according to the probability on set no more, than four consequent values of the natural series is established.
Keywords: random sequence, the maximum series of successes, limiting theorems, convergence on probability.
Mots-clés : convergence on distribution 
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     title = {On a question of limiting distribution of series in~random binary sequence},
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V. A. Barvinok; V. I. Bogdanovich; A. N. Plotnikov. On a question of limiting distribution of series in~random binary sequence. Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences, no. 4 (2012), pp. 56-71. http://geodesic.mathdoc.fr/item/VSGTU_2012_4_a5/