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Explosion phenomena in stochastic coagulation-fragmentation models. (English) Zbl 1082.60075
An acquaintance with the review of deterministic and stochastic models of aggregation and coagulation [D. J. Aldous, Bernoulli 5, 3–48 (1999; Zbl 0930.60096)] should precede the reading of the present paper. The paper addresses stochastic coalescence models where explosive jump processes are the major technical tool. After establishing general explosion criteria for pure jump processes with arbitrary locally compact separable metric space, it is proved that the mass flow process explodes almost surely in case of pure coagulation. In the study of pure multiple fragmentation for a continuous size space, explosion criteria are found for both the direct simulation model and the mass flow model, provided the total fragmentation rate grows sufficiently fast at zero. However an example shows that explosion properties of both models are inequivalent.

MSC:
60J75 Jump processes (MSC2010)
60K40 Other physical applications of random processes
82D60 Statistical mechanics of polymers
70F16 Collisions in celestial mechanics, regularization
70F35 Collision of rigid or pseudo-rigid bodies
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