Dynamics of infinite age-structured populations / A Markov process for an infinite interacting particle system in the continuum

(1) Dominika Jasińska (Maria Curie-Sklodowska University, Lublin, and MIM UW, Poland) "Dynamics of infinite age-structured populations": Abstract: A Markov evolution of an infinite age-structured population of migrants is studied. Its members are point entities characterized by their spatial location and age – time of presence. They can arrive and depart from a continuous habitat. The dynamics is described by means of correlation functions. It is show that the corresponding evolution equation has a unique solution, which is obtained in an explicit way.

(2) Jurij Kozicki (Maria Curie-Sklodowska University, Lublin, Poland) "A Markov process for an infinite interacting particle system in the continuum" - the work with Michael Roeckner (Bielefeld): Abstract: An infinite system of point particles placed in a continuous habitat is studied. Its constituents perform random jumps with mutual repulsion described by translation invariant jump kernel and interaction potential, respectively. The pure states of this system are locally finite subsets of the habitat, which can also be interpreted as locally finite Radon measures. For a special class of (sub-Poissonian) probability measures on the state space, there is proved that a restricted initial-value martingale problem employing sub-Poissonian measures has a unique solution. Thereby, a Markov process with cadlag paths is constructed that describes the stochastic evolution of the considered particle system.