| Autor: |
Baccelli, Francois, Mathieu, Fabien, Norros, Ilkka |
| Rok vydání: |
2014 |
| Předmět: |
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| Druh dokumentu: |
Working Paper |
| Popis: |
This paper is focused on a class of spatial birth and death process of the Euclidean space where the birth rate is constant and the death rate of a given point is the shot noise created at its location by the other points of the current configuration for some response function $f$. An equivalent view point is that each pair of points of the configuration establishes a random connection at an exponential time determined by $f$, which results in the death of one of the two points. We concentrate on space-motion invariant processes of this type. Under some natural conditions on $f$, we construct the unique time-stationary regime of this class of point processes by a coupling argument. We then use the birth and death structure to establish a hierarchy of balance integral relations between the factorial moment measures. Finally, we show that the time-stationary point process exhibits a certain kind of repulsion between its points that we call $f$-repulsion. |
| Databáze: |
arXiv |
| Externí odkaz: |
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