An extension of the Tusnady inequality for general distributions

Ion Grama (1)

1 LMBA - Laboratoire de Mathématiques de Bretagne Atlantique

Under mild assumptions an analog of Tusnady's inequality for conditional distributions of partial sums of independent nonidentically distributed r.v.'s is obtained. These type of inequalities provide very sharp bounds for couplings of random variables via quantile transformations, which are main tools for proving various strong invariance principles for sums of independent random variables.

Domaines: Probabilités [math.PR]

Ion Grama. An extension of the Tusnady inequality for general distributions. The 14th Conference on Aplied and Industrial Mathematics. (Satellite Conference of ICM 2006.) , The Romanian Society of Applied and Industrial Mathematics (ROMAI), Mathematical Society of the Republic of Moldova, Moldova State University, Tiraspol State University, Institute of Mathematics and Computer Science of the Academy of Sciences of Moldova and the Center for Education and Research in Mathematics and Computer Science at Moldova State University, Aug 2006, Chisinau, Moldova. pp.184-188. ⟨hal-01270357⟩