PDF files of articles are only available for institutions which have paid for the online version upon signing an Institutional User License.

On convergence of the empirical mean method for non-identically distributed random vectors

Volume 41 / 2014

E. Gordienko, J. Ruiz de Chávez, E. Zaitseva Applicationes Mathematicae 41 (2014), 1-12 MSC: Primary 90C15; Secondary 65C05. DOI: 10.4064/am41-1-1

Abstract

We consider the following version of the standard problem of empirical estimates in stochastic optimization. We assume that the underlying random vectors are independent and not necessarily identically distributed but that they satisfy a “slow variation” condition in the sense of the definition given in this paper. We show that these assumptions along with the usual restrictions (boundedness and equicontinuity) on a class of functions allow one to use the empirical mean method to obtain a consistent sequence of estimates of infimums of the functional to be minimized. Also, we provide certain estimates of the rate of convergence.

Authors

  • E. GordienkoDepartment of Mathematics
    Universidad Autónoma
    Metropolitana-Iztapalapa
    San Rafael Atlixco 186
    Col. Vicentina
    C.P. 09340, Mexico City, México
    e-mail
  • J. Ruiz de ChávezDepartment of Mathematics
    Universidad Autónoma
    Metropolitana-Iztapalapa
    San Rafael Atlixco 186
    Col. Vicentina
    C.P. 09340, Mexico City, México
    e-mail
  • E. ZaitsevaInstituto Tecnológico Autónomo
    de México
    Rio Hondo 1
    Col. Progreso Tizapan
    Del. Alvaro Obregón
    C.P. 01080, Mexico City, México
    e-mail

Search for IMPAN publications

Query phrase too short. Type at least 4 characters.

Rewrite code from the image

Reload image

Reload image