Universal Bounds and Monotonicity Properties of Ratios of Hermite and Parabolic Cylinder Functions

Torben Koch
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Torben Koch: Center for Mathematical Economics, Bielefeld University

No 615, Center for Mathematical Economics Working Papers from Center for Mathematical Economics, Bielefeld University

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. Diff erently 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 infi nitesimal generator of the Ornstein-Uhlenbeck process. As a byproduct, we obtain Turán type inequalities.

Keywords: Hermite functions; parabolic cylinder functions; Turáan type inequalities; Ornstein-Uhlenbeck process (search for similar items in EconPapers)
Date: 2019-05-22
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Citations: View citations in EconPapers (2)

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Persistent link: https://EconPapers.repec.org/RePEc:bie:wpaper:615

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