Weak Stability of Centred Quadratic Stochastic Operators

We consider the weak convergence of iterates of so-called centred quadratic stochastic operators. These iterations allow us to study the discrete time evolution of probability distributions of vector-valued traits in populations of inbreeding or hermaphroditic species, whenever the offspring’s trait is equal to an additively perturbed arithmetic mean of the parents’ traits. It is shown that for the existence of a weak limit, it is sufficient that the distributions of the trait and the perturbation have a finite variance or have tails controlled by a suitable power function. In particular, probability distributions from the domain of attraction of stable distributions have found an application, although in general the limit is not stable.

Keywords

ASYMPTOTIC STABILITY DYADIC STABILITY INFINITE DIVISIBLE DISTRIBUTIONS QUADRATIC STOCHASTIC OPERATORS WEAK CONVERGENCE

Publication year

Publication language

angielski

Journal title / conference title

Bulletin of the Malaysian Mathematical Sciences Society

Publication country

Malezja

Page numbers [from-to]

1813 - 1830

Author (3)




Organization unit

Department of Mathematics
Instytut Informatyki Stosowanej im.Krzysztofa Brzeskiego
Katedra Rachunku Prawdopodobieństwa i Biomatematyki

Faculty

Państwowa Wyższa Szkoła Zawodowa w Elblągu
Uppsala University, Sweden
Wydział Fizyki Technicznej i Matematyki Stosowanej