|
This article is cited in 3 scientific papers (total in 3 papers)
Repetitions of the values of a function of segments of a sequence of independent trials
A. M. Shoitov
Abstract:
We consider the problem on the number $\xi(N)$ of $k$-fold matchings
of symbols that occur in a sequence of random variables resulting from
aggregating the states of a Markov–Bruns chain generated by $n$-tuples
$(X_i,\dots,X_{i+n-1})$ consisting of elements of the sequence
$(X_1,\dots,X_{N+n-1})$ of independent realisations of a random
variable $X$. The aggregation of states consists of applying
a given function $f$, which takes a finite number of values,
to the $n$-tuples $(X_i,\dots,X_{i+n-1})$.
We prove a theorem on convergence to a multivariate normal law
for the joint distribution of $\xi(N)$ under various
aggregation functions, and give sufficient conditions on convergence
of the distribution of $\xi(N)$ to the chi-square law as
$N\to\infty$. These results are applied to the problem
on $k$-fold imperfect matchings of $n$-tuples in a sequence
of polynomial trials. In particular, we prove a theorem on convergence
to a multivariate normal law for the vector
of numbers of $k$-fold imperfect matchings of various lengths and ranks.
Received: 15.02.2000
Citation:
A. M. Shoitov, “Repetitions of the values of a function of segments of a sequence of independent trials”, Diskr. Mat., 12:3 (2000), 49–59; Discrete Math. Appl., 10:4 (2000), 379–389
Linking options:
https://www.mathnet.ru/eng/dm345https://doi.org/10.4213/dm345 https://www.mathnet.ru/eng/dm/v12/i3/p49
|
|