Alsedà–Misiurewicz systems with place-dependent probabilities*The research was supported by the Polish Ministry of Science and Higher Education 'Diamond Grant' 0090/DIA/2017/46. (8th October 2020)

• Record Type: Journal Article
• Authors: Czudek, Klaudiusz
• Is Part Of: Nonlinearity. Volume 33:Number 11(2020)
• Page Start: 6221
• Page End: 6243
• Publication Date: 2020-10-08
• Subjects: iterated function systems -- place-dependent probabilities -- Markov chains -- Alsedà–Misiurewicz systems; primary 37E05 -- 60G10 -- 60J05; Nonlinear theories -- Periodicals; Mathematical analysis -- Periodicals; Mathematical analysis; Nonlinear theories; Periodicals; 515
• DOI: 10.1088/1361-6544/aba094
• Languages: English
• ISSNs: 0951-7715

Abstract

Abstract: We consider systems of two specific piecewise linear homeomorphisms of the unit interval, so called Alsedà–Misiurewicz systems, and investigate the basic properties of Markov chains which arise when these two transformations are applied randomly with probabilities depending on the point of the interval. Though this iterated function system is not contracting in average and known methods do not apply, stability and the strong law of large numbers are proven.