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Interacting Point Processes
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DOI：10.1007/s10959-026-01502-8.png)
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Abstract
En 中文
We study two different types of vector point processes with interacting components, introducing a migration-type effect. The first case concerns two groups which modify their states with rate functions depending on time only. This yields a representation of the vector process in terms of independent non-homogeneous Skellam processes. In the general case, the decomposition involves independent Poisson processes. The second model is a birth-death-migration vector process. In the case of the linear death-migration we show that for a fixed time instant, the vector is equal in distribution to the sum of two independent multinomial random variables. As a by-product, we derive the distribution of a pure migration process. Finally, we study the described vector processes time-changed with the inverse of Bernstein subordinators, establishing a general result concerning the relationship between fractional difference-differential equations and the probability mass function of a wider class of point processes.
Keywords:
Non-homogeneous Skellam process
Birth-death process
Migration process
Convolution-type derivative
Inverse subordinators
Journal
J
IF:
0.6
Papers:
64
Citations:
0