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Compatible Linear Lypunov Function for Infinite Dimensional Volterra Quadratic Stochastic Operators

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Infinite Dimensional Analysis, Quantum Probability and Applications (ICQPRT 2021)

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Abstract

The simplest non-linear operator is the quadratic ones. Most of the researches in this direction were investigating on finite set of all probability distributions. However, there are models where the probability distributions are countably infinite, which means that the considered operators are defined on infinite-dimensional spaces. We restrict ourselves to Quadratic Stochastic Operators (QSOs) define on infinite dimension, specifically a class of QSOs called Volterra. In this paper, we construct a linear Lyapunov function for infinite dimensional Volterra QSOs by means of finite dimensional ones.

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Acknowledgements

The author acknowledges the Ministry of Higher Education (MOHE) and Research Management Centre-UTM, Universiti Teknologi Malaysia (UTM) for the financial support through Fundamental Research Grant Scheme (FRGS/1/2021/STG06/UTM/02/5).

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Authors and Affiliations

  1. Universiti Teknologi Malaysia, 81300, Skudai, Johor Bahru, Johor, Malaysia

    Ahmad Fadillah bin Embong

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  1. Ahmad Fadillah bin Embong
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Correspondence to Ahmad Fadillah bin Embong .

Editor information

Editors and Affiliations

  1. Vito Volterra Interdepartamental Centre, Universita degli Studi di Roma, Rome, Italy

    Luigi Accardi

  2. Department of Mathematical Sciences, College of Science, United Arab Emirates University, Al Ain, Abu Dhabi, United Arab Emirates

    Farrukh Mukhamedov

  3. Department of Mathematical Sciences, College of Science, United Arab Emirates University, Al Ain, Abu Dhabi, United Arab Emirates

    Ahmed Al Rawashdeh

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bin Embong, A.F. (2022). Compatible Linear Lypunov Function for Infinite Dimensional Volterra Quadratic Stochastic Operators. In: Accardi, L., Mukhamedov, F., Al Rawashdeh, A. (eds) Infinite Dimensional Analysis, Quantum Probability and Applications. ICQPRT 2021. Springer Proceedings in Mathematics & Statistics, vol 390. Springer, Cham. https://doi.org/10.1007/978-3-031-06170-7_19

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