  We revisit two basic Direct Simulation Monte Carlo Methods to model
aggregation kinetics and extend them for aggregation processes with collisional
fragmentation (shattering). We test the performance and accuracy of the
extended methods and compare their performance with efficient deterministic
finite-difference method applied to the same model. We validate the stochastic
methods on the test problems and apply them to verify the existence of
oscillating regimes in the aggregation-fragmentation kinetics recently detected
in deterministic simulations. We confirm the emergence of steady oscillations
of densities in such systems and prove the stability of the oscillations with
respect to fluctuations and noise.
