Abstract:
We consider some problems on random correspondences related to
runs in random sequences. We find the generating functions
for the joint distributions of some characteristics of runs
in binary Markov sequences and sequences of independent random variables.
We solve the operator equations describing the distributions under consideration. The research was supported by the Russian Foundation for Basic Research,
grant 99–01–00540.
This publication is cited in the following 5 articles:
L. Ya. Saveliev, “Calculation of the number of states in binary Markov stochastic models”, Num. Anal. Appl., 8:2 (2015), 159–167
L. Ya. Savelev, S. V. Balakin, “Nekotorye primeneniya stokhasticheskoi teorii serii”, Sib. zhurn. industr. matem., 15:3 (2012), 111–123
L. Ya. Savelyev, S. V. Balakin, “A combinatorial approach to calculation of moments of characteristics of runs in ternary Markov sequences”, Discrete Math. Appl., 21:1 (2011), 47–67
L. Ja. Savel'ev, S. V. Balakin, “Joint distribution of the number of ones and the number of 1-runs in binary Markov sequences”, Discrete Math. Appl., 14:4 (2004), 353–372
L. Ja. Savel'ev, S. V. Balakin, B. V. Khromov, “Covering runs in binary Markov sequences”, Discrete Math. Appl., 13:2 (2003), 111–138