On quadratic stochastic processes and related differential equations
It is known that the theory of Markov process is a rapidly developing field with numerous applications to many branches of mathematics and physics, biology and so on. But there are some physical models which cannot be described by such processes. One of such models is related to population genetic...
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| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
Institute of Physics Publishing (UK)
2013
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| Subjects: | |
| Online Access: | http://irep.iium.edu.my/30079/1/mfaspch-JPCS%282013%29.pdf http://irep.iium.edu.my/30079/ http://dx.doi.org/10.1088/1742-6596/435/1/012013 |
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| Summary: | It is known that the theory of Markov process is a rapidly developing field with numerous
applications to many branches of mathematics and physics, biology and so on. But there are some physical
models which cannot be described by such processes. One of such models is related to population genetics.
These processes are called quadratic stochastic processes (q.s.p.). In this theory it is important to construct
nontrivial examples of such processes. In the present paper we are going to provide a construction of q.s.p.
by means of two given processes. We should stress that such a construction allows us to produce lots of
nontrivial examples of q.s.o. We also associate to given q.s.p. two kind of processes. Note that one of
such processes is Markov. It is proved that such kind of processes uniquely define q.s.p. Moreover, we also
derive some differential equations for q.s.p. |
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