The Annals of Applied Probability

Explosion phenomena in stochastic coagulation–fragmentation models

Wolfgang Wagner

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First we establish explosion criteria for jump processes with an arbitrary locally compact separable metric state space. Then these results are applied to two stochastic coagulation–fragmentation models—the direct simulation model and the mass flow model. In the pure coagulation case, there is almost sure explosion in the mass flow model for arbitrary homogeneous coagulation kernels with exponent bigger than 1. In the case of pure multiple fragmentation with a continuous size space, explosion occurs in both models provided the total fragmentation rate grows sufficiently fast at zero. However, an example shows that the explosion properties of both models are not equivalent.

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Ann. Appl. Probab., Volume 15, Number 3 (2005), 2081-2112.

First available in Project Euclid: 15 July 2005

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Primary: 60J75: Jump processes 60K40: Other physical applications of random processes

Explosion of jump processes stochastic particle systems coagulation and fragmentation models


Wagner, Wolfgang. Explosion phenomena in stochastic coagulation–fragmentation models. Ann. Appl. Probab. 15 (2005), no. 3, 2081--2112. doi:10.1214/105051605000000386.

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