Universal bounds and monotonicity properties of ratios of hermite and parabolic cylinder functions

Arbeitspapier

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 Turán type inequalities.

Angaben zum Objekt

• Sprache: Englisch

Verweise und Beziehungen

• Erschienen in: Series: Center for Mathematical Economics Working Papers ; No. 615

Klassifikation und Themen

• Klassifikation: Wirtschaft
• Thema: Hermite functions ; parabolic cylinder functions ; Turán type inequalities ; Ornstein-Uhlenbeck process

Beteiligte, Orts- und Zeitangaben

• Ereignis: Geistige Schöpfung
• (wer): Koch, Torben
• Ereignis: Veröffentlichung
• (wer): Bielefeld University, Center for Mathematical Economics (IMW)
• (wo): Bielefeld
• (wann): 2019

Weitere Informationen

• Handle: http://hdl.handle.net/10419/201640
• URN: urn:nbn:de:0070-pub-29357054
• Letzte Aktualisierung: 10.03.2025, 11:41 MEZ