Effective estimation of some oscillatory integrals related to infinitely divisible distributions

2020/10/29 by Bettin, Sandro, Drappeau, Sary
#41A60 (Primary) #60E07 #60E10 (Secondary) #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2010.15494

Abstract

We present a practical framework to prove, in a simple way, two-terms asymptotic expansions for Fourier integrals \mathcal I(t) = ∫_{\mathbb R}(\rm e^itϕ(x)-1) \rm d μ(x) where μ is a probability measure on ℝ and ϕ is measurable. This applies to many basic cases, in link with Levy's continuity theorem. We present applications to limit laws related to rational continued fractions coefficients.

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