The Annals of Applied Probability

Explosion phenomena in stochastic coagulation–fragmentation models

Wolfgang Wagner

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Abstract

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.

Article information

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

Dates
First available in Project Euclid: 15 July 2005

Permanent link to this document
https://projecteuclid.org/euclid.aoap/1121433778

Digital Object Identifier
doi:10.1214/105051605000000386

Mathematical Reviews number (MathSciNet)
MR2152254

Zentralblatt MATH identifier
1082.60075

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

Keywords
Explosion of jump processes stochastic particle systems coagulation and fragmentation models

Citation

Wagner, Wolfgang. Explosion phenomena in stochastic coagulation–fragmentation models. Ann. Appl. Probab. 15 (2005), no. 3, 2081--2112. doi:10.1214/105051605000000386. https://projecteuclid.org/euclid.aoap/1121433778


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