A Limit Theorem on a Subcritical Galton-Watson Process with Immigration

Venkataraman, K. N.; Nanthi, K.

Ann. Probab., Tome 10 (1982) no. 4, p. 1069-1074 / Harvested from Project Euclid

Résumé

For a sub-critical Galton-Watson process $\mathbf{X}$ with immigration, estimators have been studied by Pakes (1971) for the mean of the stationary distribution of $\mathbf{X}$, and by Nanthi (1979) for the offspring mean and the immigration mean of $\mathbf{X}$. These estimators have been shown by them to be asymptotically normal. In this paper it is shown that they have a joint limiting distribution which is singularly normal.

Publié le : 1982-11-14
Classification: Subcritical Galton-Watson process with immigration, limit distribution, 62M99, 60F99

@article{1176993730,
     author = {Venkataraman, K. N. and Nanthi, K.},
     title = {A Limit Theorem on a Subcritical Galton-Watson Process with Immigration},
     journal = {Ann. Probab.},
     volume = {10},
     number = {4},
     year = {1982},
     pages = { 1069-1074},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1176993730}
}

Venkataraman, K. N.; Nanthi, K. A Limit Theorem on a Subcritical Galton-Watson Process with Immigration. Ann. Probab., Tome 10 (1982) no. 4, pp.  1069-1074. http://gdmltest.u-ga.fr/item/1176993730/