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Weak Stability of Centred Quadratic Stochastic Operators
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Analysis and Probability Theory. Linkoping Univ, Dept Comp & Informat Sci, S-58183 Linkoping, Sweden.ORCID iD: 0000-0002-5816-4345
State Univ Appl Sci Elblag, Krzysztof Brzeski Inst Appl Informat, Ul Wojska Polskiego 1, PL-82300 Elblag, Poland.
Gdansk Univ Technol, Dept Probabil & Biomath, Ul Narutowicza 11-12, PL-80233 Gdansk, Poland.
2019 (English)In: BULLETIN OF THE MALAYSIAN MATHEMATICAL SCIENCES SOCIETY, ISSN 0126-6705, Vol. 42, no 4, p. 1813-1830Article in journal (Refereed) Published
Abstract [en]

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.

Place, publisher, year, edition, pages
MALAYSIAN MATHEMATICAL SCIENCES SOC , 2019. Vol. 42, no 4, p. 1813-1830
Keywords [en]
Asymptotic stability, Dyadic stability, Infinite divisible distributions, Quadratic stochastic operators, Weak convergence
National Category
Probability Theory and Statistics
Identifiers
URN: urn:nbn:se:uu:diva-390084DOI: 10.1007/s40840-017-0575-8ISI: 000471896200032OAI: oai:DiVA.org:uu-390084DiVA, id: diva2:1340601
Funder
Knut and Alice Wallenberg FoundationSwedish Institute, 11142/2013Swedish Institute, 19826/2014Swedish Institute, 00507/2012Available from: 2019-08-06 Created: 2019-08-06 Last updated: 2019-08-06Bibliographically approved

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