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• W2945254055 abstract "We obtain so far unproved properties of a ratio involving a class of Hermite and parabolic cylinder functions. Those ratios are shown to be strictly decreasing and bounded by universal constants. Differently to usual analytic approaches, we employ simple purely probabilistic arguments to derive our results. In particular, we exploit the relation between Hermite and parabolic cylinder functions and the eigenfunctions of the infinitesimal generator of the Ornstein-Uhlenbeck process. As a byproduct, we obtain Turan type inequalities." @default.
• W2945254055 created "2019-05-29" @default.
• W2945254055 creator A5059073165 @default.
• W2945254055 date "2019-05-24" @default.
• W2945254055 modified "2023-09-27" @default.
• W2945254055 title "Universal Bounds and Monotonicity Properties of Ratios of Hermite and Parabolic Cylinder Functions." @default.
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• W2945254055 hasPublicationYear "2019" @default.
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