Some Limit Theorems on a Supercritical Simple Galton-Watson Process
Venkataraman, K. N. ; Nanthi, K.
Ann. Probab., Tome 10 (1982) no. 4, p. 1075-1078 / Harvested from Project Euclid
Text on Project Euclid
PDF
Alt PDF
Let $X = (X_n; n \geq 0; X_0 = 1)$ be a supercritical Galton-Watson process possessing an offspring mean $1 < m < \infty$, and variance $0 < \sigma^2 < \infty$. The limiting distribution of $\{X^{-1/2}_n(X_{n+r} - \hat{m}^rX_n); r = 2, \cdots, T\}$ where $\hat{m} = X_{n+1}/X_n$, is obtained. As a consequence of this result a Quenouille-Bartlett type of asymptotic goodness of fit test is also proposed for the process $X$.
Publié le : 1982-11-14
Classification:  Supercritical Galton-Watson process,  asymptotic goodness of fit test,  62M99,  60F99 
@article{1176993731,
     author = {Venkataraman, K. N. and Nanthi, K.},
     title = {Some Limit Theorems on a Supercritical Simple Galton-Watson Process},
     journal = {Ann. Probab.},
     volume = {10},
     number = {4},
     year = {1982},
     pages = { 1075-1078},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1176993731}
}

Venkataraman, K. N.; Nanthi, K. Some Limit Theorems on a Supercritical Simple Galton-Watson Process. Ann. Probab., Tome 10 (1982) no. 4, pp.  1075-1078. http://gdmltest.u-ga.fr/item/1176993731/