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Weak Stability of Centred Quadratic Stochastic Operators
Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Matematiska institutionen, Analys och sannolikhetsteori. 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 (engelsk)Inngår i: BULLETIN OF THE MALAYSIAN MATHEMATICAL SCIENCES SOCIETY, ISSN 0126-6705, Vol. 42, nr 4, s. 1813-1830Artikkel i tidsskrift (Fagfellevurdert) 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.

sted, utgiver, år, opplag, sider
MALAYSIAN MATHEMATICAL SCIENCES SOC , 2019. Vol. 42, nr 4, s. 1813-1830
Emneord [en]
Asymptotic stability, Dyadic stability, Infinite divisible distributions, Quadratic stochastic operators, Weak convergence
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Identifikatorer
URN: urn:nbn:se:uu:diva-390084DOI: 10.1007/s40840-017-0575-8ISI: 000471896200032OAI: oai:DiVA.org:uu-390084DiVA, id: diva2:1340601
Forskningsfinansiär
Knut and Alice Wallenberg FoundationSwedish Institute, 11142/2013Swedish Institute, 19826/2014Swedish Institute, 00507/2012Tilgjengelig fra: 2019-08-06 Laget: 2019-08-06 Sist oppdatert: 2019-08-06bibliografisk kontrollert

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