seminario

[Pietro Muliere <pietro.muliere@uni-bocconi.it>]

Istituto Metodi Quantitativi - Università L. Bocconi
Viale Isonzo, 25 - 20135 Milano
Tel. 02-58365629  - Fax 02-58365630



SEMINARIO

LOCAL LIMIT THEOREMS FOR SUMS OF RANDOM VARIABLES

Tengiz Shervashidze
A.Razmadze Mathematical Institute,
Tbilisi Georgia




Mercoledì, 18 dicembre, 2002 - ore 16.30
Aula Master  in Risk Management
                                 (Piano terra   Istituto IMQ)

Abstract . An approach is discussed based on the variation norm of the 
increment of a lattice distribution when having shifted it by the maximal 
span of the lattice. Examples of necessary and sufficient conditions are 
given for local limit theorem to be valid for non-identically distributed 
summands in both lattice distribution and density cases. Some 
multidimensional analogs of Levy-type 0-1 laws are discussed for random 
vectors. For a vector population with a density from a class wide enough 
convergence in variation is established to normality for the distribution 
of the system of mixed moments.Several local limit theorems are derived for 
sums of conditionaly independent random variables controlled by the finite 
ergodic Markov chain by reducing to the case of independent summands.