Titelaufnahme

Titel
Universal bounds and monotonicity properties of ratios of hermite and parabolic cylinder functions / Torben Koch
VerfasserKoch, Torben
ErschienenBielefeld, Germany : Center for Mathematical Economics (IMW), Bielefeld University, May 2019
Ausgabe
Elektronische Ressource
Umfang1 Online-Ressource (5 Seiten)
SerieCenter for Mathematical Economics Working papers ; 615
SchlagwörterHermite-Polynome In Wikipedia suchen nach Hermite-Polynome / Ornstein-Uhlenbeck-Prozess In Wikipedia suchen nach Ornstein-Uhlenbeck-Prozess
URNurn:nbn:de:hbz:6:2-121859 Persistent Identifier (URN)
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Universal bounds and monotonicity properties of ratios of hermite and parabolic cylinder functions [0.34 mb]
Zusammenfassung

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.

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