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primary topic: Regularity of 2-partition Poisson quadratic stochastic operator with three different parameters

Regularity of 2-partition Poisson quadratic stochastic operator with three different parameters
type: AcademicArticle
type: Article
abstract: Quadratic stochastic operator (QSO) was initiated by Bernstein in the early 20th century as the mathematical investigation on population genetics, involving the synthesis of Mendelian law of crossing and Galtonian law of regression. Since then, the study of QSO has been significantly developed for decades to describe dynamical systems in many areas. In this paper, we construct a Poisson quadratic stochastic operator generated by a 2-measurable partition with three different parameters defined on countable state space X=0, 1, 2, .... The main objective of this research is to study the trajectory behaviour of such operators by reducing the dynamical systems into a one-dimensional setting corresponding to the number of measurable partitions. Some cases of 2-measurable partition generated by singleton and two points with three different defined parameters will be presented. To investigate their trajectory behaviour, we may apply the functional analysis within the measure and probability theory. We shall provide both computational and analytical results, which show that the Poisson QSO generated by a 2-measurable partition with three different parameters, i.e., λl≠λ2≠λ3 is either a regular or nonregular transformation for some parameters λi∈(0, ∞) for i=1,2,3. © 2023 Author(s).
date: 2023
volume: 2692
is part of: AIP Conference Proceedings
status: peerReviewed
status: published
author list: authors
type: EPrint
type: ConferenceItemEPrint
is part of: repository

American Institute of Physics Inc.
type: Organization

AIP Conference Proceedings
type: Collection
issn: 0094243X

Nasir Ganikhodjaev
type: Person
given name: Nasir
family name: Ganikhodjaev

Nurfazatul Hazirah A. Rahman
type: Person
given name: Nurfazatul Hazirah A.
family name: Rahman

Nur Zatul Akmar Hamzah
type: Person
given name: Nur Zatul Akmar
family name: Hamzah

Muhammad Fairuz Zulkefli
type: Person
given name: Muhammad Fairuz
family name: Zulkefli

Siti Nurlaili Karim
type: Person
given name: Siti Nurlaili
family name: Karim

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primary topic: Regularity of 2-partition Poisson quadratic stochastic operator with three different parameters