Regularity of polynomial stochastic operators corresponding to graphs. (English) Zbl 1468.37046
Summary: In the present paper, we consider polynomial stochastic operators corresponding to graphs. We prove that independently on values of parameters and on initial point all trajectories converge, that is such operators have the property being regular.
MSC:
| 37H10 | Generation, random and stochastic difference and differential equations |
| 37H12 | Random iteration |
| 37N25 | Dynamical systems in biology |
| 37E25 | Dynamical systems involving maps of trees and graphs |
| 37C75 | Stability theory for smooth dynamical systems |
| 60H25 | Random operators and equations (aspects of stochastic analysis) |
| 05C05 | Trees |
| 92D10 | Genetics and epigenetics |
Keywords:
quadratic stochastic operator; polynomial stochastic operator; Cayley tree; regular operator; trajectoryReferences:
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