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arXiv · 1502.06487

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

Krzysztof Zajkowski
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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 $\ell^2$.

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Krzysztof Zajkowski. 2017-02-24. A variational formula on the Cramér function of series of independent random variables. https://doi.org/10.1007/s11117-016-0419-z

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