Representations of Invariant Measures on Multitype Galton-Watson Processes

Hoppe, Fred M.

Hoppe, Fred M.

Ann. Probab., Tome 5 (1977) no. 6, p. 291-297 / Harvested from Project Euclid

Résumé

We show that there is a one-to-one correspondence between invariant measures for the noncritical multitype Galton-Watson process and invariant measures for the single type process with a linear offspring probability generating function. Two corollaries emerge as simple applications, the first being Spitzer's Martin boundary representation, the second giving the asymptotic behaviour of the measures. Both require no extra moment assumptions and are valid for the multitype theory.

Publié le : 1977-04-14
Classification: Multitype Galton-Watson process, invariant measures, Abel's equation, Schroder's equation, Martin boundary, regular variation, conditional Yaglom limit, 60J20, 60F15

@article{1176995854,
     author = {Hoppe, Fred M.},
     title = {Representations of Invariant Measures on Multitype Galton-Watson Processes},
     journal = {Ann. Probab.},
     volume = {5},
     number = {6},
     year = {1977},
     pages = { 291-297},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1176995854}
}

Hoppe, Fred M. Representations of Invariant Measures on Multitype Galton-Watson Processes. Ann. Probab., Tome 5 (1977) no. 6, pp.  291-297. http://gdmltest.u-ga.fr/item/1176995854/