  The well known van Kampen system size expansion, while of rather general
applicability, is shown to fail to reproduce some qualitative features of the
time evolution for systems with an absorbing state, apart from a transient
initial time interval. We generalize the van Kampen ansatz by introducing a new
prescription leading to non-Gaussian fluctuations around the absorbing state.
The two expansion predictions are explicitly compared for the infinite range
voter model with speciation as a paradigmatic model with an absorbing state.
The new expansion, both for a finite size system in the large time limit and at
finite time in the large size limit, converges to to the exact solution as
obtained in a numerical implementation using the Gillespie algorithm.
Furthermore, the predicted lifetime distribution is shown to have the correct
asymptotic behavior.
