On volterra quadratic stochastic operators with continual state space

Ganikhodjaev, Nasir and Hamzah, Nur Zatul Akmar (2015) On volterra quadratic stochastic operators with continual state space. AIP Conference Proceedings , 1660 (050025). pp. 1-7. ISSN 0094-243X E-ISSN 1551-7616

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Abstract

Let FX ),( be a measurable space, and FXS ),( be the set of all probability measures on FX ),( where X is a state space and F is V - algebraon X . We consider a nonlinear transformation (quadratic stochastic operator) defined by ³³ X X ( O)( OO ydxdAyxPAV )()(),,() , where AyxP ),,( is regarded as a function of two variables x and y with fixed � FA . A quadratic stochastic operator V is called a regular, if for any initial measure the strong limit lim O)( nnV fo is exists. In this paper, we construct a family of quadratic stochastic operators defined on the segment X > @1,0 with Borel V - algebra F on X, prove their regularity and show that the limit measure is a Dirac measure.

Item Type:	Article (Journal)
Additional Information:	4430/42991
Uncontrolled Keywords:	Quadratic stochastic operator; regular; strong limit; Dirac measure.
Subjects:	Q Science > QA Mathematics
Kulliyyahs/Centres/Divisions/Institutes (Can select more than one option. Press CONTROL button):	Kulliyyah of Science > Department of Computational and Theoretical Sciences
Depositing User:	Prof. Nasir Ganikhodjaev
Date Deposited:	26 May 2015 10:07
Last Modified:	17 Feb 2017 17:59
URI:	http://irep.iium.edu.my/id/eprint/42991

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