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Universal Bounds and Monotonicity Properties of Ratios of Hermite and Parabolic Cylinder Functions

Author

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  • Koch, Torben

    (Center for Mathematical Economics, Bielefeld University)

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. 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.

Suggested Citation

  • Koch, Torben, 2019. "Universal Bounds and Monotonicity Properties of Ratios of Hermite and Parabolic Cylinder Functions," Center for Mathematical Economics Working Papers 615, Center for Mathematical Economics, Bielefeld University.
    • Handle: RePEc:bie:wpaper:615
    as

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    File URL: https://pub.uni-bielefeld.de/download/2935705/2935706
    File Function: First Version, 2019
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    References listed on IDEAS

    as
    1. Ferrari, Giorgio & Koch, Torben, 2018. "An optimal extraction problem with price impact," Center for Mathematical Economics Working Papers 603, Center for Mathematical Economics, Bielefeld University.
    2. Dirk Becherer & Todor Bilarev & Peter Frentrup, 2016. "Optimal Liquidation under Stochastic Liquidity," Papers 1603.06498, arXiv.org, revised Nov 2017.
    3. Giorgio Ferrari & Torben Koch, 2018. "An Optimal Extraction Problem with Price Impact," Papers 1812.01270, arXiv.org.
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    Cited by:

    1. Torben Koch & Tiziano Vargiolu, 2019. "Optimal Installation of Solar Panels with Price Impact: a Solvable Singular Stochastic Control Problem," Papers 1911.04223, arXiv.org.

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