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August 2005 Explosion phenomena in stochastic coagulation–fragmentation models
Wolfgang Wagner
Ann. Appl. Probab. 15(3): 2081-2112 (August 2005). DOI: 10.1214/105051605000000386


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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Wolfgang Wagner. "Explosion phenomena in stochastic coagulation–fragmentation models." Ann. Appl. Probab. 15 (3) 2081 - 2112, August 2005.


Published: August 2005
First available in Project Euclid: 15 July 2005

zbMATH: 1082.60075
MathSciNet: MR2152254
Digital Object Identifier: 10.1214/105051605000000386

Primary: 60J75 , 60K40

Keywords: coagulation and fragmentation models , Explosion of jump processes , Stochastic particle systems

Rights: Copyright © 2005 Institute of Mathematical Statistics


Vol.15 • No. 3 • August 2005
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