Geodesic
The square root law in the embedding detection problem for Markov chains with unknown matrix of transition probabilities\footnote{The paper is published by the recommendation of the Program Commitee of the CTCrypt'2016 Conference.}
Diskretnaya Matematika, Tome 29 (2017) no. 3, pp. 24-37.

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We consider the classical model of embeddings in a simple binary Markov chain with unknown transition probability matrix. We obtain conditions on the asymptotic growth of lengths of the original and embedded sequences sufficient for the consistency of the proposed statistical embedding detection test.
Keywords: Markov chain, embeddings, statistical test. 
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A. V. Volgin. The square root law in the embedding detection problem for Markov chains with unknown matrix of transition probabilities\footnote{The paper is published by the recommendation of the Program Commitee of the CTCrypt'2016 Conference.}. Diskretnaya Matematika, Tome 29 (2017) no. 3, pp. 24-37. http://geodesic.mathdoc.fr/item/DM_2017_29_3_a1/

[1] Borovkov A. A., Probability Theory, Gordon Breach, New York, 1998, 474 pp. | MR | Zbl

[2] Ivanov V. A., “Modeli vkraplenii v odnorodnye sluchainye posledovatelnosti”, Trudy po diskretnoi matematike, 11 (2008), 18–34

[3] Ivchenko G.I., Medvedev Yu.I., Vvedenie v matematicheskuyu statistiku, LKI, Moskva, 2010, 600 pp.

[4] Cramer H., Mathematical Methods of Statistics, Prinseton University Press, 1962, 590 pp. | MR | MR

[5] Ponomarev K. I., “A parametric model of embedding and its statistical analysis”, Discrete Math. Appl., 19:6 (2009), 587–596 | DOI | DOI | MR | Zbl

[6] Kharin Yu. S., Vecherko E. V., “Statistical estimation of parameters for binary Markov chain models with embeddings”, Discrete Math. Appl., 23:2 (2013), 153–169 | DOI | DOI | MR | Zbl

[7] Kharin Yu. S., Vecherko E. V., “Detection of embeddings in binary Markov chains”, Discrete Math. Appl., 26:1 (2016), 13–29 | DOI | DOI | MR | MR | Zbl

[8] Shoitov A. M., “O vyyavlenii fakta zashumleniya konechnoi tsepi Markova s neizvestnoi matritsei perekhodnykh veroyatnostei”, Prikladnaya diskretnaya matematika. Prilozhenie, 3 (2010), 44–45

[9] Filler T., Ker A.D., Fridrich J., “The square root law of steganographic capacity for Markov covers”, Proc. SPIE, 7254 (2009), 31–47

[10] Ker A.D., “A capacity result for batch steganography”, IEEE Signal Processing Letters, 14(8) (2007), 525–528 | DOI

[11] Sharp T., “An implementation of key-based digital signal steganography”, Proc. Information Hiding Workshop, 2137 (2001), 13–26 | DOI | Zbl