A LOCAL LIMIT-THEOREM ON THE SEMIDIRECT PRODUCT OF R-ASTERISK(+) AND R(D)

Authors
LEPAGE E PEIGNE M
Citation
E. Lepage et M. Peigne, A LOCAL LIMIT-THEOREM ON THE SEMIDIRECT PRODUCT OF R-ASTERISK(+) AND R(D), Annales de l'I.H.P. Probabilites et statistiques, 33(2), 1997, pp. 223-252
Citations number
19
Categorie Soggetti
Statistic & Probability","Statistic & Probability
Journal title
Annales de l'I.H.P. Probabilites et statistiques → ACNP
ISSN journal
02460203
Volume
33
Issue
2
Year of publication
1997
Pages
223 - 252
Database
ISI
SICI code
0246-0203(1997)33:2<223:ALLOTS>2.0.ZU;2-3
Abstract
Let G be the semi-direct product of R(+) and R(d) and mu a probabilit y measure on G. Let mu(n) be the nth power of convolution of mu. Unde r quite general assumptions on mu, one proves that there exists rho is an element of ]0, 1] such that the sequence of Radon measures (n(3/2) /rho(n) mu(n)) n greater than or equal to 1 converges weakly to a non -degenerate measure; furthermore, if mu(2)(n) is the marginal of mu(* n) on R(d), the sequence of Radon measures (root n/rho(n) mu(2)(n)) n greater than or equal to 1 converges weakly to a non-degenerate measu re.