Dynamics of nonlinear stochastic operators and associated Markov measures

Author:

Jamilov Uygun123,Mukhamedov Farrukh4,Mukhamedova Farzona5,Souissi Abdessatar6ORCID

Affiliation:

1. New Uzbekistan University Tashkent Uzbekistan

2. V.I. Romanovskiy Institute of Mathematics Uzbekistan Academy of Sciences Tashkent Uzbekistan

3. Faculty of Mathematics National University of Uzbekistan Tashkent Uzbekistan

4. Department of Mathematical Sciences, College of Science United Arab Emirates University Al Ain United Arab Emirates

5. King's College London London UK

6. Department of Management Information Systems, College of Business and Economics Qassim University Buraydah Saudi Arabia

Abstract

The aim of this paper is to examine the stability of a class of nonlinear stochastic operators on a finite‐dimensional simplex. We identify a number of properties of the set of the class of stochastic operators, including the stability of each operator. We then use these operators to define non‐homogeneous Markov measures that rely on initial data and carry out an investigation into the absolute continuity and singularity of these measures.

Publisher

Wiley

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