An inhomogeneous first--order integer--valued autoregressive (INAR(1))
process is investigated, where the autoregressive type coefficient slowly
converges to one. It is shown that the process converges weakly to a Poisson or
a compound Poisson distribution.Comment: Latex2e pdfeTex Version 3, 22 pages, submitted to ACTA Sci. Math.
(Szeged