On stable b-bistochastic quadratic stochastic operators and associated non-homogenous Markov chains

Farrukh Mukhamedov, Ahmad Fadillah Embong

Research output: Contribution to journalArticlepeer-review

5 Citations (Scopus)

Abstract

In the present paper, we consider a class of quadratic stochastic operators (q.s.o.) called b-bistochastic q.s.o. defined on a finite dimensional simplex. We include several properties of b-bistochastic q.s.o. and their dynamical behaviour. One of the main findings in this paper is the description on the uniqueness of the fixed points. Besides, we list the conditions on strict contractive b-bistochastic q.s.o. on low-dimensional simplices, and it turns out that, the uniqueness of the fixed point does not imply its strict contractivity. Finally, we associate non-homogeneous Markov measures with b-bistochastic q.s.o. The defined measures were proven to satisfy the mixing property for regular b-bistochastic q.s.o. Moreover, we show that non-homogeneous Markov measures associated with a class of b-bistochastic q.s.o on one-dimensional simplex, meet the absolute continuity property.

Original languageEnglish
Pages (from-to)1-21
Number of pages21
JournalLinear and Multilinear Algebra
Volume66
Issue number1
DOIs
Publication statusPublished - Jan 2 2018

Keywords

  • Quadratic stochastic operators
  • absolute continuity
  • b-bistochastic
  • b-order
  • mixing
  • unique fixed point

ASJC Scopus subject areas

  • Algebra and Number Theory

Fingerprint

Dive into the research topics of 'On stable b-bistochastic quadratic stochastic operators and associated non-homogenous Markov chains'. Together they form a unique fingerprint.

Cite this