BRANCHING PROCESSES WITH INTERACTIONS: SUBCRITICAL COOPERATIVE REGIME
Por:
Gonzalez Casanova, Adrian, Carlos Pardo, Juan, Luis Perez, Jose
Publicada:
1 mar 2021
Resumen:
In this paper, we introduce a family of processes with values on the
nonnegative integers that describes the dynamics of populations where
individuals are allowed to have different types of interactions. The
types of interactions that we consider include pairwise interactions,
such as competition, annihilation, and cooperation; and interactions
among several individuals that can be viewed as catastrophes. We call
such families of processes branching processes with interactions. Our
aim is to study their long-term behaviour under a specific regime of the
pairwise interaction parameters that we introduce as the subcritical
cooperative regime. Under such a regime, we prove that a process in this
class comes down from infinity and has a moment dual which turns out to
be a jump-diffusion that can be thought as the evolution of the
frequency of a trait or phenotype, and whose parameters have a classical
interpretation in terms of population genetics. The moment dual is an
important tool for characterizing the stationary distribution of
branching processes with interactions whenever such a distribution
exists; it is also an interesting object in its own right.
Filiaciones:
Gonzalez Casanova, Adrian:
Univ Nacl Autonoma Mexico, Inst Matemat, Area Invest Cient, Ciudad Univ, Mexico City 04510, DF, Mexico
Carlos Pardo, Juan:
AND, Mexico City, DF, Mexico
Ctr Invest Matemat AC, Calle Jalisco S-N,Apartado Postal 402, Guanajuato 36023, Gto, Mexico
Luis Perez, Jose:
Ctr Invest Matemat, Mexico City, DF, Mexico
Ctr Invest Matemat AC, Calle Jalisco S-N,Apartado Postal 402, Guanajuato 36023, Gto, Mexico
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