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

A variational formula on the Cramér function of series of independent random variables In (Zajkowski, Positivity 19:529–537, 2015) 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 $$\ell ^1$$ ℓ 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 $$\ell ^2$$ ℓ 2 . http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Positivity Springer Journals

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

, Volume 21 (1) – May 4, 2016
10 pages

/lp/springer_journal/a-variational-formula-on-the-cram-r-function-of-series-of-independent-yzrgnPOG3Q
Publisher
Springer International Publishing
Subject
Mathematics; Fourier Analysis; Operator Theory; Potential Theory; Calculus of Variations and Optimal Control; Optimization; Econometrics
ISSN
1385-1292
eISSN
1572-9281
D.O.I.
10.1007/s11117-016-0419-z
Publisher site
See Article on Publisher Site

### Abstract

In (Zajkowski, Positivity 19:529–537, 2015) 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 $$\ell ^1$$ ℓ 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 $$\ell ^2$$ ℓ 2 .

### Journal

PositivitySpringer Journals

Published: May 4, 2016

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