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Stochastic order and attractiveness for particle systems with multiple births, deaths and jumps. (English) Zbl 1228.60104
The need for realistic models of metapopulation dynamics systems [I. Hanski, (1999)] motivates the present investigation of birth, death and migration processes that refer to more than one particle per unit of time. Concepts of stochastic order and attrractiveness are borrowed from T. Gobbon and E. Saada [Ann. Inst. Henri PoincarĂ©, Probab. Stat. 46, No. 4, 1132–1177 (2010; Zbl 1252.60093)]. Coupled random processes are considered with a focus on attractiveness and ergodcity (existence of a unique invariant measure). For a class of processes, sufficient and necessary conditions for attractiveness are established. Major applications refer to specific reaction-diffusion processes, multitype contact processes and conservative dynamics. Ergodicity conditions are set for an individual recovery epidemic model.

60K35 Interacting random processes; statistical mechanics type models; percolation theory
82C22 Interacting particle systems in time-dependent statistical mechanics
60J80 Branching processes (Galton-Watson, birth-and-death, etc.)
60J75 Jump processes (MSC2010)
37A30 Ergodic theorems, spectral theory, Markov operators
92D25 Population dynamics (general)
92D30 Epidemiology
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