Convolution Inequalities with Probability Distributions
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Abstract
There are many results related to inequalities linked to convolutions. We can create a new probability distribution from well-known probability distributions. One of the classical method is addition. If we want to find the probability distribution of the sum of two independent probability random variables then we need to find the convolution of their distributions. In this paper, I computed the upper bound of the convolution of several several independent random variables: Normal Distributions and Exponential Distributions.
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References
David F. Anderson, Timo Sepppalainen and Benedek Valko,“Introduction to Probability”, Cambridge, https://doi.org/10.1017/9781108235310
Richard C. Barnard, Stefan Steinerberger, “Three Convolution Inequalities on the Real Line with Connections to Additive Combinatorics”, Journal of Number Theory 207, p. 42-55 (2020)
SABUROU SAITOH, VU KIM TUAN, AND MASAHIRO YAMAMOTO, “CONVOLUTION INEQUALITIES AND APPLICATIONS”, Journal of Inequalities in Pure and Applied Mathematics, Volume 4, Issue 3, Article 50, (2003)
Eric A. Carlen, Ian Jauslin, Elliott H. Lieb, Michael P. Loss, ”On the convolution inequality". International Mathematics Research Notices, Oxford University Press (OUP), http://dx.doi.org/10.1093/imrn/rnaa350 (2021)