This article is cited in
2 papers
On the uniqueness of the moment problem in the class of $q$-distributions
A. N. Alekseichuk
Abstract:
We introduce the notion of
$\overline{q}=(q_1,\ldots,q_t)$-binomial invariants
of a random vector
$\overline{\xi}=(\xi_1,\ldots,\xi_t)$ distributed on
the set of vectors whose
$i$th coordinate is a non-negative integer power
of the number
$q_i>1$,
$i=1,\ldots,t$. We find relations between
$\overline{q}$-binomial invariants and mixed moments, give conditions under which
the distribution of the vector
$\overline{\xi}$ is uniquely determined
by the sequence of its
$\overline{q}$-binomial invariants, and present
expressions of probabilities
$$
\mathsf P(\xi_1=q_1^{r_1},\ldots,\xi_t=q_t^{r_t}),\qquad
r_1,\ldots,r_t=0,1,\ldots,
$$
in terms of the corresponding
$\overline{q}$-binomial invariants and estimates
of these probabilities. We prove a theorem on convergence of a sequence
of distributions of such random vectors under the condition that the corresponding
$\overline{q}$-binomial invariants converge.
The results obtained are used in the study of the limit distribution
of the number of solutions of a class of systems of linear equations
over a finite field.
UDC:
512.21
Received: 28.06.1996
DOI:
10.4213/dm406
Fulltext:
PDF file (1046 kB)