On volterra quadratic stochastic operators with continual state space
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...
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American Institute of Physics
2015
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| Online Access: | http://irep.iium.edu.my/42991/ http://irep.iium.edu.my/42991/ http://irep.iium.edu.my/42991/ http://irep.iium.edu.my/42991/1/Paper_Nur_Zatul_2015_AIP.pdf |
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iium-429912017-02-17T09:59:11Z http://irep.iium.edu.my/42991/ On volterra quadratic stochastic operators with continual state space Ganikhodjaev, Nasir Hamzah, Nur Zatul Akmar QA Mathematics 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. American Institute of Physics 2015-05 Article PeerReviewed application/pdf en http://irep.iium.edu.my/42991/1/Paper_Nur_Zatul_2015_AIP.pdf 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 http://dx.dori.og/10.1063/1.4915658 10.1063/1.4915658 |
| 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 Ganikhodjaev, Nasir Hamzah, Nur Zatul Akmar On volterra quadratic stochastic operators with continual state space |
| description |
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. |
| format |
Article |
| author |
Ganikhodjaev, Nasir Hamzah, Nur Zatul Akmar |
| author_facet |
Ganikhodjaev, Nasir Hamzah, Nur Zatul Akmar |
| author_sort |
Ganikhodjaev, Nasir |
| title |
On volterra quadratic stochastic operators with continual state space |
| title_short |
On volterra quadratic stochastic operators with continual state space |
| title_full |
On volterra quadratic stochastic operators with continual state space |
| title_fullStr |
On volterra quadratic stochastic operators with continual state space |
| title_full_unstemmed |
On volterra quadratic stochastic operators with continual state space |
| title_sort |
on volterra quadratic stochastic operators with continual state space |
| publisher |
American Institute of Physics |
| publishDate |
2015 |
| url |
http://irep.iium.edu.my/42991/ http://irep.iium.edu.my/42991/ http://irep.iium.edu.my/42991/ http://irep.iium.edu.my/42991/1/Paper_Nur_Zatul_2015_AIP.pdf |
| first_indexed |
2023-09-18T21:01:14Z |
| last_indexed |
2023-09-18T21:01:14Z |
| _version_ |
1777410637801979904 |