Quadratic stochastic operators and processes: results and open problems

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

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Abstract

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.

Item Type:	Article (Journal)
Additional Information:	5537/1612
Uncontrolled Keywords:	Quadratic stochastic operator; quadratic stochastic process; quantum quadratic stochastic operator; quantum quadratic stochastic process; fixed point; trajectory; Volterra and non-Volterra operators; ergodic; simplex.
Subjects:	Q Science > QA Mathematics
Kulliyyahs/Centres/Divisions/Institutes (Can select more than one option. Press CONTROL button):	Kulliyyah of Science Kulliyyah of Science > Department of Computational and Theoretical Sciences
Depositing User:	Dr. Farrukh Mukhamedov
Date Deposited:	05 Sep 2011 16:13
Last Modified:	22 Nov 2011 08:52
URI:	http://irep.iium.edu.my/id/eprint/1612

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