  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.
