Please use this identifier to cite or link to this item: http://hdl.handle.net/10419/201640
Authors: 
Koch, Torben
Year of Publication: 
2019
Series/Report no.: 
Center for Mathematical Economics Working Papers No. 615
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. 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.
Subjects: 
Hermite functions
parabolic cylinder functions
Turán type inequalities
Ornstein-Uhlenbeck process
Persistent Identifier of the first edition: 
Document Type: 
Working Paper

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