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Prevalence Problem in the Set of Quadratic Stochastic Operators Acting on \(L^{1}\)

  • Krzysztof BartoszekEmail author
  • Małgorzata Pułka
Article

Abstract

This paper is devoted to the study of the problem of prevalence in the class of quadratic stochastic operators acting on the \(L^{1}\) space for the uniform topology. We obtain that the set of norm quasi-mixing quadratic stochastic operators is a dense and open set in the topology induced by a very natural metric. This shows the typical long-term behaviour of iterates of quadratic stochastic operators.

Keywords

Quadratic stochastic operators Nonhomogeneous Markov operators Baire category Mixing nonlinear Markov process 

Mathematics Subject Classification

47A35 47B65 47B07 54H20 92B99 92D15 

Notes

Acknowledgments

We would like to acknowledge Wojciech Bartoszek for many helpful comments and insights.

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Copyright information

© Malaysian Mathematical Sciences Society and Universiti Sains Malaysia 2015

Authors and Affiliations

  1. 1.Department of MathematicsUppsala UniversityUppsalaSweden
  2. 2.Department of Probability and BiomathematicsGdańsk University of TechnologyGdańskPoland

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