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- Title
Weak Stability of Centred Quadratic Stochastic Operators.
- Authors
Bartoszek, Krzysztof; Domsta, Joachim; Pułka, Małgorzata
- Abstract
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.
- Subjects
ARITHMETIC mean; TAILS
- Publication
Bulletin of the Malaysian Mathematical Sciences Society, 2019, Vol 42, Issue 4, p1813
- ISSN
0126-6705
- Publication type
Article
- DOI
10.1007/s40840-017-0575-8