Author： Pelletier M.
Publisher： Academic Press
ISSN： 0047-259X
Source： Journal of Multivariate Analysis, Vol.71, Iss.1, 1999-10, pp. : 76-93
Disclaimer: Any content in publications that violate the sovereignty, the constitution or regulations of the PRC is not accepted or approved by CNPIEC.
Abstract
We prove an almost sure central limit theorem for some multidimensional stochastic algorithms used for the search of zeros of a function and known to satisfy a central limit theorem. The almost sure version of the central limit theorem requires either a logarithmic empirical mean (in the same way as in the case of independent identically distributed variables) or another scale, depending on the choice of the algorithm gains.
Related content
Access to resources
Recommend
Critical Behavior in Almost Sure Central Limit Theory
Journal of Theoretical Probability, Vol. 20, Iss. 3, 2007-09 ,pp. :
Almost sure functional limit theorem for the product of partial sums
ESAIM: Probability and Statistics, Vol. 14, Iss. issue, 2010-10 ,pp. :
Almost Sure Central Limit Theorems for Heavily Trimmed Sums
Acta Mathematica Sinica, Vol. 20, Iss. 5, 2004-09 ,pp. :