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...

Full description

Bibliographic Details
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/ http://irep.iium.edu.my/1612/ http://irep.iium.edu.my/1612/ http://irep.iium.edu.my/1612/1/mfgrru-idaqp%282011%29.pdf

id	iium-1612
recordtype	eprints
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
repository_type	Digital Repository
institution_category	Local University
institution	International Islamic University Malaysia
building	IIUM Repository
collection	Online Access
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/ http://irep.iium.edu.my/1612/ http://irep.iium.edu.my/1612/ http://irep.iium.edu.my/1612/1/mfgrru-idaqp%282011%29.pdf
first_indexed	2023-09-18T20:09:01Z
last_indexed	2023-09-18T20:09:01Z
_version_	1777407351865737216

Quadratic stochastic operators and processes: results and open problems

Similar Items