A certain branching random walk, $\{X_i\}$, on a compact group or a compact homogeneous space is studied. It is proved that the sums $\sum^n_0f(X_i)$ are asymptotically normally distributed for all nice functions $f$ if and only if the Fourier coefficients of the transition probability distribution have real parts not exceeding $\frac{1}{2}$.
Publié le : 1983-11-14
Classification:
Branching random walks,
compact groups,
limit theorems,
60J80,
60B15,
60J15,
60F05
@article{1176993441,
author = {Janson, Svante},
title = {Limit Theorems for Certain Branching Random Walks on Compact Groups and Homogeneous Spaces},
journal = {Ann. Probab.},
volume = {11},
number = {4},
year = {1983},
pages = { 909-930},
language = {en},
url = {http://dml.mathdoc.fr/item/1176993441}
}
Janson, Svante. Limit Theorems for Certain Branching Random Walks on Compact Groups and Homogeneous Spaces. Ann. Probab., Tome 11 (1983) no. 4, pp. 909-930. http://gdmltest.u-ga.fr/item/1176993441/