Conditional principles for random weighted measures

Nathael Gozlan (1)

1 Laboratoire d'Analyse et de Mathématiques Appliquées

Let (Zn)n∈N be a sequence of real i.i.d. random variables and (xi,n)i=1,...,n;n∈N a double-indexed sequence of elements of some compact metric space X. The author studies the limiting behaviour of the weighted random measures Ln=1n∑ni=1Ziδxi,n. In particular, the so-called Gibbs conditioning principle is obtained and the results of F. Gamboa and É. Gassiat [Ann. Statist. 25 (1997), no. 1, 328-350; MR1429928 (98k:62002)] are extended.

Domaines: Probabilités [math.PR]

Nathael Gozlan. Conditional principles for random weighted measures. ESAIM: Probability and Statistics, 2005, 9 (1), pp.283--306. ⟨10.1051/ps:2005016⟩. ⟨hal-00795831⟩