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Abstract
The Markov dynamics of an infinite continuum birth-and-death system of point particles with age is studied. Each particle is characterized by its location \(x\in \mathbb{R}^d\) and age \(a_x\geq 0\). The birth and death rates of a particle are age dependent. The states of the system are described in terms of probability measures on the corresponding configuration space. The exact solution of the evolution equation for the correlation functions of first and second orders is found.
Highlights
We describe the Markov evolution of a continuum infinite system of particles with an age structure
An infinite continuum particle system can provide a good model for the evolution of atoms, dust grains, water droplets and molecules
The states of the system are probability measures on the corresponding configuration spaces, the Markov evolution of which is obtained by solving a Fokker–Planck equation
Summary
We describe the Markov evolution of a continuum infinite system of particles with an age structure. An infinite continuum particle system can provide a good model for the evolution of atoms, dust grains, water droplets and molecules. Such models with an age structure can describe stellar systems, like galaxies, or large communities of infected individuals. The most important facts on the approach we follow in this work can be found in [1, 4, 7, 12] In this approach, the states of the system are probability measures on the corresponding configuration spaces, the Markov evolution of which is obtained by solving a Fokker–Planck equation.
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