Further reading
Preston, S. H., Heuveline, P. and Guillot, M. 2001. Demography: Measuring and Modelling Population Processes. Oxford: Blackwell. Chapter 8.
The initial and most important application of generalized stable population methods to demographic estimation is the ‘synthetic extinct generations’ method for the evaluation of the completeness of registered deaths against a census count after adjusting for population growth that was first proposed by Bennett and Horiuchi in 1981. An up-to-date description of the method can be found here:
Dorrington R. E. 2013. Synthetic extinct generations, in Moultrie T. A., R. E. Dorrington, A. G. Hill, K. H. Hill, I. M. Timæus and B. Zaba (eds), Tools for Demographic Estimation. Paris: International Union for the Scientific Study of Population. http://demographicestimation.iussp.org/content/synthetic-extinct-generations-methods 
References
Bennett, N. G. and S. Horiuchi. 1981. Estimating the completeness of death registration in a closed population, Population Index 47(2): 202-221.
Preston, S. H. 1987. Estimation of certain measures in family demography based upon generalized stable population relations, in J. Bongaarts, T. K. Burch, and K. W. Wachter (eds.), Family Demography: Methods and their Application. International Studies in Demography. Oxford: Clarendon, pp. 40-62.
Preston, S. H. 1987. Relations among standard epidemiologic measures in a population. American Journal of Epidemiology 126(2): 336-345.
Preston, S. H. and N. G. Bennett. 1983. A census-based method for estimating adult mortality, Population Studies 37(1): 91-104.
Preston, S. H. and A. J. Coale. 1982. Age structure, growth, attrition and accession: A new synthesis, Population Index 48(2): 217-259.