Abstract:
We find conditions which are sufficient for convergence of the distribution of
the number of matches of values of a function considered on tuples of arguments taken
from a sequence of independent identically distributed random variables
to the Poisson law and estimate the convergence rate.
We derive a series of corollaries of this result. In particular, in the equiprobable
polynomial scheme we obtain Poisson limit theorems for the number of pairs of
non-overlapping tuples with identical frequencies of occurrences of symbols
and for the number of pairs of tuples with identical structure. This research was supported by the Program of President of Russian Federation
for supporting young Russian scientists, grant 2831.2003.09.
Citation:
A. M. Shoitov, “The Poisson approximation for the number of matches of values of a discrete function from chains”, Diskr. Mat., 17:2 (2005), 56–69; Discrete Math. Appl., 15:3 (2005), 241–254
\Bibitem{Sho05}
\by A.~M.~Shoitov
\paper The Poisson approximation for the number of matches of values of a discrete function from chains
\jour Diskr. Mat.
\yr 2005
\vol 17
\issue 2
\pages 56--69
\mathnet{http://mi.mathnet.ru/dm98}
\crossref{https://doi.org/10.4213/dm98}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2167800}
\zmath{https://zbmath.org/?q=an:1113.60029}
\elib{https://elibrary.ru/item.asp?id=9135423}
\transl
\jour Discrete Math. Appl.
\yr 2005
\vol 15
\issue 3
\pages 241--254
\crossref{https://doi.org/10.1515/156939205774464512}
Linking options:
https://www.mathnet.ru/eng/dm98
https://doi.org/10.4213/dm98
https://www.mathnet.ru/eng/dm/v17/i2/p56
This publication is cited in the following 7 articles:
V. G. Mikhailov, N. M. Mezhennaya, “Normal approximation for U- and V-statistics of a stationary absolutely regular sequence”, Sib. elektron. matem. izv., 17 (2020), 672–682
Vladimir G. Mikhaylov, “Estimates of accuracy of the Poisson approximation for the distribution of number of runs of long string repetitions in a Markov chain”, Discrete Math. Appl., 26:2 (2016), 105–113
V. G. Mikhailov, A. M. Shoitov, “Mnogokratnye povtoreniya dlinnykh tsepochek v konechnoi tsepi Markova”, Matem. vopr. kriptogr., 6:3 (2015), 117–133
V. G. Mikhailov, A. M. Shoitov, “On repetitions of long tuples in a Markov chain”, Discrete Math. Appl., 25:5 (2015), 295–303
V. G. Mikhailov, A. M. Shoitov, “O chislakh mnozhestv ekvivalentnykh tsepochek v posledovatelnosti nezavisimykh sluchainykh velichin”, Matem. vopr. kriptogr., 4:1 (2013), 77–86
A. M. Shoitov, “Strukturno ekvivalentnye tsepochki v ravnoveroyatnoi polinomialnoi skheme”, Matem. vopr. kriptogr., 3:3 (2012), 129–151
A. M. Shoitov, “The compound Poisson distribution of the number of matches of values of a discrete function of s-tuples in segments of a sequence of random variables”, Discrete Math. Appl., 17:3 (2007), 209–230
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