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...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
American Institute of Physics
2015
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| Subjects: | |
| 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 |
| Summary: | 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. |
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