A variational formula on the Cramér function of series of independent random variables
Tóm tắt
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
$$\ell ^1$$
. 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
$$\ell ^2$$
.
Tài liệu tham khảo
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