We explore the asymptotic behavior of densities of sums of independent random variables that are convoluted with a small continuous noise.
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∗Received by the editors December 20, 2018. The research of the first author was partially supported by NSF grant DMS-1855575. Originally published in the Russian journal Teoriya Veroy-atnostei i ee Primeneniya, 65 (2020), pp. 79–102. https://doi.org/10.1137/S0040585X97T989829 †School of Mathematics, University of Minnesota, Minneapolis, MN 55455 (email@example.com. edu). ‡Department of Mathematics, University of Florida, Gainesville, FL 32611 (a.marsiglietti@ufl. edu).
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- Central limit theorem
- Local limit theorem