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arXiv · 1305.1860

(Quasi)additivity properties of the Legendre--Fenchel transform and its inverse, with applications in probability

Iosif Pinelis
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Abstract

The notion of the Hölder convolution is introduced. The main result is that, under general conditions on functions L_1, ..., L_n, the function inverse to the Legendre--Fenchel transform of the Hölder convolution of L_1, ..., L_n coincides with the sum of the inverses of the Legendre--Fenchel transforms of the individual functions L_1, ..., L_n. Applications to probability theory are presented. In particular, an upper bound on the quantiles of the distribution of the sum of random variables is given.

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Iosif Pinelis. 2013-06-03. (Quasi)additivity properties of the Legendre--Fenchel transform and its inverse, with applications in probability. https://arxiv.org/abs/1305.1860

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