On a question of limiting distribution of series in random binary sequence
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 pro...
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| Format: | Article |
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Samara State Technical University
2012-12-01
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| Series: | Vestnik Samarskogo Gosudarstvennogo Tehničeskogo Universiteta. Seriâ: Fiziko-Matematičeskie Nauki |
| Online Access: | http://mi.mathnet.ru/eng/vsgtu1192 |
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doaj-c09decab984f492188034f4a32f502502020-11-24T21:41:24ZengSamara State Technical UniversityVestnik Samarskogo Gosudarstvennogo Tehničeskogo Universiteta. Seriâ: Fiziko-Matematičeskie Nauki1991-86152310-70812012-12-014(29)567110.14498/vsgtu1192On a question of limiting distribution of series in random binary sequence V. A. BarvinokV. I. BogdanovichA. N. PlotnikovLimiting 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.http://mi.mathnet.ru/eng/vsgtu1192 |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
V. A. Barvinok V. I. Bogdanovich A. N. Plotnikov |
| spellingShingle |
V. A. Barvinok V. I. Bogdanovich A. N. Plotnikov On a question of limiting distribution of series in random binary sequence Vestnik Samarskogo Gosudarstvennogo Tehničeskogo Universiteta. Seriâ: Fiziko-Matematičeskie Nauki |
| author_facet |
V. A. Barvinok V. I. Bogdanovich A. N. Plotnikov |
| author_sort |
V. A. Barvinok |
| title |
On a question of limiting distribution of series in random binary sequence |
| title_short |
On a question of limiting distribution of series in random binary sequence |
| title_full |
On a question of limiting distribution of series in random binary sequence |
| title_fullStr |
On a question of limiting distribution of series in random binary sequence |
| title_full_unstemmed |
On a question of limiting distribution of series in random binary sequence |
| title_sort |
on a question of limiting distribution of series in random binary sequence |
| publisher |
Samara State Technical University |
| series |
Vestnik Samarskogo Gosudarstvennogo Tehničeskogo Universiteta. Seriâ: Fiziko-Matematičeskie Nauki |
| issn |
1991-8615 2310-7081 |
| publishDate |
2012-12-01 |
| description |
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. |
| url |
http://mi.mathnet.ru/eng/vsgtu1192 |
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AT vabarvinok onaquestionoflimitingdistributionofseriesinrandombinarysequence AT vibogdanovich onaquestionoflimitingdistributionofseriesinrandombinarysequence AT anplotnikov onaquestionoflimitingdistributionofseriesinrandombinarysequence |
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