Weak Stability of Centred Quadratic Stochastic OperatorsWe 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.ASYMPTOTIC STABILITYDYADIC STABILITYINFINITE DIVISIBLE DISTRIBUTIONSQUADRATIC STOCHASTIC OPERATORSWEAK CONVERGENCE2019angielskiWeak Stability of Centred Quadratic Stochastic OperatorsMalezja1813 - 1830Krzysztof Bartoszek Joachim Domsta Małgorzata Pułka