Long-term behavior of a critical multitype spatially homogeneous branching particle process and a related reaction-diffusion system
- Fleischmann, Klaus
- Vatutin, Vladimir A.
2010 Mathematics Subject Classification
- 60J80 60J15
- extinction, survival, persistence, systems of reaction-diffusion equations, steady state, genealogical tree, reduced tree, marked particle
A dichotomy concerning extinction and survival (even persistence) at late times is established for critical multitype spatially homogeneous branching particle systems in continuous time under natural conditions on the branching mechanism known from the "classical" processes without motion component. This generalizes results of López-Mimbela and Wakolbinger [LMW96] and others. Our simplified approach is based on some genealogical tree analysis combined with the study of the long-term behavior of L1-norms of solutions of related systems of reaction-"diffusion" equations, which is perhaps also of some independent interest.
- Probab. Theory Related Fields, 116, (2000), pp. 545-572