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Article Dans Une Revue Ramanujan Journal Année : 2022

Effective estimation of some oscillatory integrals related to infinitely divisible distributions

Résumé

We present a practical framework to prove, in a simple way, two-terms asymptotic expansions for Fourier integrals $$ {\mathcal I}(t) = \int_{\mathbb R}({\rm e}^{it\phi(x)}-1) {\rm d} \mu(x) $$ where $\mu$ is a probability measure on $\mathbb{R}$ and $\phi$ 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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Dates et versions

hal-02998544 , version 1 (10-11-2020)
hal-02998544 , version 2 (03-02-2022)

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Citer

Sandro Bettin, Sary Drappeau. Effective estimation of some oscillatory integrals related to infinitely divisible distributions. Ramanujan Journal, 2022, 57 (2), pp.849-861. ⟨10.1007/s11139-020-00362-y⟩. ⟨hal-02998544v2⟩
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