We present a practical framework to prove, in a simple way, two-term asymptotic expansions for Fourier integrals I(t)=∫R(eitϕ(x)-1)dμ(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 fraction coefficients.
Effective estimation of some oscillatory integrals related to infinitely divisible distributions
Bettin S.;Drappeau S.
2022-01-01
Abstract
We present a practical framework to prove, in a simple way, two-term asymptotic expansions for Fourier integrals I(t)=∫R(eitϕ(x)-1)dμ(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 fraction coefficients.
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