TY  - GEN
AB  - 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.
DA  - 2019
KW  - Hermite functions
KW  - parabolic cylinder functions
KW  - Turáan type inequalities
KW  - Ornstein-Uhlenbeck process
LA  - eng
PY  - 2019
SN  - 0931-6558
TI  - Universal Bounds and Monotonicity Properties of Ratios of Hermite and Parabolic Cylinder Functions
UR  - https://nbn-resolving.org/urn:nbn:de:0070-pub-29357054
Y2  - 2024-11-24T12:28:14
ER  -