If the means and variances of a sequence of random variables converge, and all semiinvariants (cumulants) of sufficiently high order tend to zero, then the variables converge in distribution to a normal distribution. Thus no information is needed on the remaining (finitely many) semiinvariants. This is applied to give a new criterion for asymptotic normality of sums of dependent variables. An example is included where this criterion is applied to the number of induced subgraphs of a particular type in a random graph.
Publié le : 1988-01-14
Classification:
Convergence in distribution,
central limit theorem,
semiinvariants,
cumulants,
method of moments,
random graphs,
60F05,
05C80
@article{1176991903,
author = {Janson, Svante},
title = {Normal Convergence by Higher Semiinvariants with Applications to Sums of Dependent Random Variables and Random Graphs},
journal = {Ann. Probab.},
volume = {16},
number = {4},
year = {1988},
pages = { 305-312},
language = {en},
url = {http://dml.mathdoc.fr/item/1176991903}
}
Janson, Svante. Normal Convergence by Higher Semiinvariants with Applications to Sums of Dependent Random Variables and Random Graphs. Ann. Probab., Tome 16 (1988) no. 4, pp. 305-312. http://gdmltest.u-ga.fr/item/1176991903/