caa a22 4500 378930494 CHVBK 20180305123628.0 cr unu---uuuuu 161128e20040801xx s 000 0 eng 10.1515/1569392041938802 doi (NATIONALLICENCE)gruyter-10.1515/1569392041938802 The joint distribution of the number of ones and the number of 1-runs in binary Markov sequences [Elektronische Daten] [L. Ya. Savelyev, S. V. Balakin] We describe the distributions of the number of ones, the number of runs of ones in a binary Markov sequence and their joint distribution. We find the generating functions of the distributions under consideration, calculate the means, variances and covariances. For these moments we give explicit and asymptotic formulas with estimates of accuracy. Formulas for the Gaussian approximations are also derived. We consider the corresponding operator equations. In this connection we describe a special model of random walks. Copyright 2004, Walter de Gruyter Savelyev L. Ya aut Balakin S. V. aut Discrete Mathematics and Applications Walter de Gruyter 14/4(2004-08-01), 353-372 0924-9265 14:4<353 2004 14 dma https://doi.org/10.1515/1569392041938802 text/html Onlinezugriff via DOI 1 research article jats NATIONALLICENCE 856 40 https://doi.org/10.1515/1569392041938802 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Savelyev L. Ya aut NATIONALLICENCE 700 1- Balakin S. V. aut NATIONALLICENCE 773 0- Discrete Mathematics and Applications Walter de Gruyter 14/4(2004-08-01), 353-372 0924-9265 14:4<353 2004 14 dma CC0 http://creativecommons.org/publicdomain/zero/1.0 nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-gruyter