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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| Format: | Article |
| Language: | English |
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World Scientific Publishing
2011
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| Online Access: | http://irep.iium.edu.my/1612/ http://irep.iium.edu.my/1612/1/mfgrru-idaqp%282011%29.pdf |
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| author | Ganikhodzaev, Rasul Mukhamedov, Farrukh Rozikov, Utkir Abdulloevich |
| author_facet | Ganikhodzaev, Rasul Mukhamedov, Farrukh Rozikov, Utkir Abdulloevich |
| author_sort | Ganikhodzaev, Rasul |
| building | IIUM Repository |
| collection | Online Access |
| 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. |
| first_indexed | 2025-11-14T14:21:17Z |
| format | Article |
| id | iium-1612 |
| institution | International Islamic University Malaysia |
| institution_category | Local University |
| language | English |
| last_indexed | 2025-11-14T14:21:17Z |
| publishDate | 2011 |
| publisher | World Scientific Publishing |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | iium-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 PeerReviewed 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 |
| spellingShingle | QA Mathematics Ganikhodzaev, Rasul Mukhamedov, Farrukh Rozikov, Utkir Abdulloevich Quadratic stochastic operators and processes: results and open problems |
| title | 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_short | Quadratic stochastic operators and processes: results and open problems |
| title_sort | quadratic stochastic operators and processes: results and open problems |
| topic | QA Mathematics |
| url | http://irep.iium.edu.my/1612/ http://irep.iium.edu.my/1612/ http://irep.iium.edu.my/1612/ http://irep.iium.edu.my/1612/1/mfgrru-idaqp%282011%29.pdf |