UNIVERSAL BOUNDS AND MONOTONICITY PROPERTIES OF RATIOS OF HERMITE AND PARABOLIC CYLINDER FUNCTIONS

Koch T (2020)
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY 148(5): 2149-2155.

Zeitschriftenaufsatz | E-Veröff. vor dem Druck | 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. Differently from the 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.
Stichworte
Hermite functions; parabolic cylinder functions; Turan-type; inequalities; Ornstein-Uhlenbeck process
Erscheinungsjahr
2020
Zeitschriftentitel
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY
Band
148
Ausgabe
5
Seite(n)
2149-2155
ISSN
0002-9939
eISSN
1088-6826
Page URI
https://pub.uni-bielefeld.de/record/2942714

Zitieren

Koch T. UNIVERSAL BOUNDS AND MONOTONICITY PROPERTIES OF RATIOS OF HERMITE AND PARABOLIC CYLINDER FUNCTIONS. PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY. 2020;148(5):2149-2155.
Koch, T. (2020). UNIVERSAL BOUNDS AND MONOTONICITY PROPERTIES OF RATIOS OF HERMITE AND PARABOLIC CYLINDER FUNCTIONS. PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 148(5), 2149-2155. doi:10.1090/proc/14896
Koch, T. (2020). UNIVERSAL BOUNDS AND MONOTONICITY PROPERTIES OF RATIOS OF HERMITE AND PARABOLIC CYLINDER FUNCTIONS. PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY 148, 2149-2155.
Koch, T., 2020. UNIVERSAL BOUNDS AND MONOTONICITY PROPERTIES OF RATIOS OF HERMITE AND PARABOLIC CYLINDER FUNCTIONS. PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 148(5), p 2149-2155.
T. Koch, “UNIVERSAL BOUNDS AND MONOTONICITY PROPERTIES OF RATIOS OF HERMITE AND PARABOLIC CYLINDER FUNCTIONS”, PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, vol. 148, 2020, pp. 2149-2155.
Koch, T.: UNIVERSAL BOUNDS AND MONOTONICITY PROPERTIES OF RATIOS OF HERMITE AND PARABOLIC CYLINDER FUNCTIONS. PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY. 148, 2149-2155 (2020).
Koch, Torben. “UNIVERSAL BOUNDS AND MONOTONICITY PROPERTIES OF RATIOS OF HERMITE AND PARABOLIC CYLINDER FUNCTIONS”. PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY 148.5 (2020): 2149-2155.

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