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

Koch T (2019) Center for Mathematical Economics Working Papers; 615.
Bielefeld: Center for Mathematical Economics.

Diskussionspapier | Veröffentlicht | Englisch

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Abstract / Bemerkung
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.
Stichworte
Hermite functions; parabolic cylinder functions; Turáan type inequalities; Ornstein-Uhlenbeck process
Erscheinungsjahr
2019
Serientitel
Center for Mathematical Economics Working Papers
Band
615
ISSN
0931-6558
Page URI
https://pub.uni-bielefeld.de/record/2935705

### Zitieren

Koch T. Universal Bounds and Monotonicity Properties of Ratios of Hermite and Parabolic Cylinder Functions. Center for Mathematical Economics Working Papers. Vol 615. Bielefeld: Center for Mathematical Economics; 2019.
Koch, T. (2019). Universal Bounds and Monotonicity Properties of Ratios of Hermite and Parabolic Cylinder Functions (Center for Mathematical Economics Working Papers, 615). Bielefeld: Center for Mathematical Economics.
Koch, T. (2019). Universal Bounds and Monotonicity Properties of Ratios of Hermite and Parabolic Cylinder Functions. Center for Mathematical Economics Working Papers, 615, Bielefeld: Center for Mathematical Economics.
Koch, T., 2019. Universal Bounds and Monotonicity Properties of Ratios of Hermite and Parabolic Cylinder Functions, Center for Mathematical Economics Working Papers, no.615, Bielefeld: Center for Mathematical Economics.
T. Koch, Universal Bounds and Monotonicity Properties of Ratios of Hermite and Parabolic Cylinder Functions, Center for Mathematical Economics Working Papers, vol. 615, Bielefeld: Center for Mathematical Economics, 2019.
Koch, T.: Universal Bounds and Monotonicity Properties of Ratios of Hermite and Parabolic Cylinder Functions. Center for Mathematical Economics Working Papers, 615. Center for Mathematical Economics, Bielefeld (2019).
Koch, Torben. Universal Bounds and Monotonicity Properties of Ratios of Hermite and Parabolic Cylinder Functions. Bielefeld: Center for Mathematical Economics, 2019. Center for Mathematical Economics Working Papers. 615.
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