Depts for Mathematics at the Univ of Szeged - Bezdány Dániel: Asymptotic behaviour of critical decomposable 3-type Galton-Watson processes with immigration having triangular offspring mean matrix with diagonal entries 1

$help$

$See by year$	$See by month$	$Jump to month$
See by year	See by month	Jump to month

Bezdány Dániel: Asymptotic behaviour of critical decomposable 3-type Galton-Watson processes with immigration having triangular offspring mean matrix with diagonal entries 1

$Download as iCal file$

$Export Event$ Export Event

Preserve formatting in description (only supported in some calendar applications)

Wednesday, 8. May 2024, 14:00 - 16:00

Abstract: We study the asymptotic behaviour of a critical decomposable 3-type Galton-Watson process with immigration when its offspring mean matrix is triangular with diagonal entries 1. It is proved that, under second or fourth order moment assumptions on the offspring and immigration distributions, a sequence of appropriately scaled random step processes formed from such a Galton-Watson process converges weakly. The limit process can be described using independent squared Bessel processes, the linear combinations of their integral processes, and possibly their double integral processes. The presence of the double integral process in the limit distribution is a new phenomenon in the description of asymptotic behavior of critical multi-type Galton-Watson processes with immigration. Our results complete and extend some results of Foster and Ney (1978) for some strongly critical decomposable 3-type Galton-Watson processes with immigration.

Back