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Diskr. Mat., 2016, Volume 28, Issue 2, Pages 92–107 (Mi dm1372)  

Limit theorems for the number of successes in random binary sequences with random embeddings

B. I. Selivanov, V. P. Chistyakov

Steklov Mathematical Institute of Russian Academy of Sciences, Moscow

Abstract: The sequence of $ n $ random $ (0,1) $-variables $ X_1, \ldots   ,   X_n $ is considered, with $ \theta_n $ of these variables distributed equiprobable and the others take the value 1 with probability $ p $ ($ 0 < p < 1, p \neq 1/2 $), $\theta_n $ is a random variable taking values $ 0, 1, \ldots , n $). On the assumption that $ n \to \infty $ and under certain conditions imposed on $ p,\theta_n $ and $ X_k, k = 1,\ldots, n, $ several limit theorems for the sum $ S_n = \sum_{k=1}^n X_k $. The results are of interest in connection with steganography and statistical analysis of sequences produced by random number generators.

Keywords: random binary sequence, random sum, random embeddings, steganography, convergence in distribution} \classification[Funding]{This work was supported by the RAS program «Modern problems in theoretic mathematics».

Funding Agency Grant Number
Russian Academy of Sciences - Federal Agency for Scientific Organizations
This work was supported by the RAS program "Modern problems in theoretic mathematics".


DOI: https://doi.org/10.4213/dm1372

Full text: PDF file (524 kB)
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English version:
Discrete Mathematics and Applications, 2016, 26:6, 355–367

Bibliographic databases:

UDC: 519.214+519.212.2
Received: 07.04.2016

Citation: B. I. Selivanov, V. P. Chistyakov, “Limit theorems for the number of successes in random binary sequences with random embeddings”, Diskr. Mat., 28:2 (2016), 92–107; Discrete Math. Appl., 26:6 (2016), 355–367

Citation in format AMSBIB
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\paper Limit theorems for the number of successes in random binary sequences with random embeddings
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\pages 92--107
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