Geodesic
On the longest head-run in an~individual random sequence
Teoriâ veroâtnostej i ee primeneniâ, Tome 42 (1997) no. 3, pp. 608-615

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In the framework of the Kolmogorov approach to verifying the theory of probability an analysis of a result of S. S. Samarova on the length of the longest head-run for the Markov chain with two states is given. This result is a refinement and generalization of P. Erdös and P. Revesz's corresponding results. An analogous assertion is formulated and proved for individual random sequences. A complexity characterization of its application is also given.
Keywords: laws of large numbers, length of runs, individual random sequence, Kolmogorov complexity.
Mots-clés : Markov chain 
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     author = {V. V. V'yugin},
     title = {On the longest head-run in an~individual random sequence},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {608--615},
     publisher = {mathdoc},
     volume = {42},
     number = {3},
     year = {1997},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_1997_42_3_a11/}
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V. V. V'yugin. On the longest head-run in an~individual random sequence. Teoriâ veroâtnostej i ee primeneniâ, Tome 42 (1997) no. 3, pp. 608-615. http://geodesic.mathdoc.fr/item/TVP_1997_42_3_a11/