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Quadratic stochastic operators and processes: results and open problems

The history of the quadratic stochastic operators can be traced back to the work of Bernshtein (1924). For more than 80 years, this theory has been developed and many papers were published. In recent years it has again become of interest in connection with its numerous applications in many branches...

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Main Authors: Ganikhodzaev, Rasul, Mukhamedov, Farrukh, Rozikov, Utkir Abdulloevich
Format: Article
Language:English
Published: World Scientific Publishing 2011
Subjects:
QA Mathematics
Online Access:http://irep.iium.edu.my/1612/1/mfgrru-idaqp%282011%29.pdf
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spelling my.iium.irep.16122011-11-22T00:52:31Z http://irep.iium.edu.my/1612/ Quadratic stochastic operators and processes: results and open problems Ganikhodzaev, Rasul Mukhamedov, Farrukh Rozikov, Utkir Abdulloevich QA Mathematics The history of the quadratic stochastic operators can be traced back to the work of Bernshtein (1924). For more than 80 years, this theory has been developed and many papers were published. In recent years it has again become of interest in connection with its numerous applications in many branches of mathematics, biology and physics. But most results of the theory were published in non-English journals, full text of which are not accessible. In this paper we give all necessary definitions and a brief description of the results for three cases: (i) discrete-time dynamical systems generated by quadratic stochastic operators; (ii) continuous-time stochastic processes generated by quadratic operators; (iii) quantum quadratic stochastic operators and processes. Moreover, we discuss several open problems. World Scientific Publishing 2011 Article REM application/pdf en http://irep.iium.edu.my/1612/1/mfgrru-idaqp%282011%29.pdf Ganikhodzaev, Rasul and Mukhamedov, Farrukh and Rozikov, Utkir Abdulloevich (2011) Quadratic stochastic operators and processes: results and open problems. Infinite Dimensional Analysis, Quantum Probability and Related Topics, 14 (2). pp. 279-335. ISSN 0219-0257 http://www.worldscinet.com/idaqp/mkt/sampleiss.shtml doi:10.1142/S0219025711004365
institution Universiti Islam Antarabangsa Malaysia
building IIUM Library
collection Institutional Repository
continent Asia
country Malaysia
content_provider International Islamic University Malaysia
content_source IIUM Repository (IREP)
url_provider http://irep.iium.edu.my/
language English
topic QA Mathematics
spellingShingle QA Mathematics
Ganikhodzaev, Rasul
Mukhamedov, Farrukh
Rozikov, Utkir Abdulloevich
Quadratic stochastic operators and processes: results and open problems
description The history of the quadratic stochastic operators can be traced back to the work of Bernshtein (1924). For more than 80 years, this theory has been developed and many papers were published. In recent years it has again become of interest in connection with its numerous applications in many branches of mathematics, biology and physics. But most results of the theory were published in non-English journals, full text of which are not accessible. In this paper we give all necessary definitions and a brief description of the results for three cases: (i) discrete-time dynamical systems generated by quadratic stochastic operators; (ii) continuous-time stochastic processes generated by quadratic operators; (iii) quantum quadratic stochastic operators and processes. Moreover, we discuss several open problems.
format Article
author Ganikhodzaev, Rasul
Mukhamedov, Farrukh
Rozikov, Utkir Abdulloevich
author_facet Ganikhodzaev, Rasul
Mukhamedov, Farrukh
Rozikov, Utkir Abdulloevich
author_sort Ganikhodzaev, Rasul
title Quadratic stochastic operators and processes: results and open problems
title_short Quadratic stochastic operators and processes: results and open problems
title_full Quadratic stochastic operators and processes: results and open problems
title_fullStr Quadratic stochastic operators and processes: results and open problems
title_full_unstemmed Quadratic stochastic operators and processes: results and open problems
title_sort quadratic stochastic operators and processes: results and open problems
publisher World Scientific Publishing
publishDate 2011
url http://irep.iium.edu.my/1612/1/mfgrru-idaqp%282011%29.pdf
http://irep.iium.edu.my/1612/
http://www.worldscinet.com/idaqp/mkt/sampleiss.shtml
_version_ 1643604821214756864
score 13.211869

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