A variational formula on the Cramér function of series of independent random variables

Abstract

In [11] it has been proved some variational formula on the Legendre-Fenchel transform of the cumulant generating function (the Cramér function) of Rademacher series with coefficients in the space ${\ell }^1$. In this paper we show a generalization of this formula to series of a larger class of any independent random variables with coefficients that belong to the space ${\ell }^2$.

arXiv comment10 pages