Projective surjectivity of quadratic stochastic operators on L1 and its application

Farrukh Mukhamedov, O. Khakimov, A. Fadillah Embong

Research output: Contribution to journalArticlepeer-review

Abstract

A nonlinear Markov chain is a discrete time stochastic process whose transitions depend on both the current state and the current distribution of the process. The nonlinear Markov chain over an infinite state space can be identified by a continuous mapping (the so-called nonlinear Markov operator) defined on a set of all probability distributions (which is a simplex). In the present paper, we consider a continuous analogue of the mentioned mapping acting on L1-spaces. Main aim of the current paper is to investigate projective surjectivity of quadratic stochastic operators (QSO) acting on the set of all probability measures. To prove the main result, we study the surjectivity of infinite dimensional nonlinear Markov operators and apply them to the projective surjectivity of the considered QSO. Furthermore, the obtained results are applied to the existence of the positive solution of some Hammerstein integral equations.

Original languageEnglish
Article number111034
JournalChaos, Solitons and Fractals
Volume148
DOIs
Publication statusPublished - Jul 2021

Keywords

  • Nonlinear equation
  • Projective surjection
  • Quadratic stochastic operator

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematics(all)
  • Physics and Astronomy(all)
  • Applied Mathematics

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