2020/01/18 by Dominika Jasińska, Yuri Kozitsky, Jasinska, Dominika +1
Mathematics · Medicine · #Stochastic processes and statistical mechanics #Mathematical and Theoretical Epidemiology and Ecology Models #Random Matrices and Applications
paper · pdf · doi:10.48550/arxiv.2001.06706
The Markov evolution is studied of an infinite age-structured population of migrants arriving in and departing from a continuous habitat X ⊆\mathdsRd -- at random and independently of each other. Each population member is characterized by its age a≥ 0 (time of presence in the population) and location x∈ X. The population states are probability measures on the space of the corresponding marked configurations. The result of the paper is constructing the evolution μ0 → μt of such states by solving a standard Fokker-Planck equation for this models. We also found a stationary state μ existing if the emigration rate is separated away from zero. It is then shown that μt weakly converges to μ as t→ +∞.