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- Title
A Markov process for an infinite age-structured population.
- Authors
Jasińska, Dominika; Kozitsky, Yuri
- Abstract
A Markov process is constructed in an explicit way for an infinite system of entities arriving in and departing from a habitat X, which is a locally compact Polish space with a positive Radon measure χ. Along with its location x ∈ X, each particle is characterized by age α ≥ 0 - time since arriving. As the state space one takes the set of marked configurations ..., equipped with a metric that makes it a complete and separable metric space. The stochastic evolution of the system is described by a Kolmogorov operator L, expressed through the measure χ and a departure rate m(x, α) ≥ 0, and acting on bounded continuous functions F : ... → ℝ. For this operator, we pose the martingale problem and show that it has a unique solution, explicitly constructed in the paper. We also prove that the corresponding process has a unique stationary state and is temporarily egrodic if the rate of departure is separated away from zero.
- Subjects
MARKOV processes; INFINITY (Mathematics); RADON measures; KOLMOGOROV complexity; MARTINGALES (Mathematics); ERGODIC theory
- Publication
ALEA. Latin American Journal of Probability & Mathematical Statistics, 2022, Vol 19, Issue 1, p467
- ISSN
1980-0436
- Publication type
Article
- DOI
10.30757/ALEA.v19-18