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Pré-Publication, Document De Travail Année : 2019

Bounds of derivatives of the solution of the Stein equation for the generalized inverse Gaussian and Kummer distributions

Résumé

For regular test functions h, we prove that all the derivatives of the solution of the Stein equation for the generalized inverse Gaussian and Kummer distributions are bounded. In order to complete the results in [6] where the authors have established an upper bound of the solution and its first and second derivatives of the Stein equation for the generalized inverse Gaussian and Kummer distributions, we provide an explicit upper bound of the third derivative of these solutions. Furthermore, for k ≥ 4, by doing a stepwise calculation, we express the bound of the k-th derivative as a function of the bounds of the derivatives of lower order.
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Dates et versions

hal-02419186 , version 1 (19-12-2019)
hal-02419186 , version 2 (19-12-2019)

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  • HAL Id : hal-02419186 , version 2

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Essomanda Konzou, Efoevi Angelo Koudou, Kossi E Gneyou. Bounds of derivatives of the solution of the Stein equation for the generalized inverse Gaussian and Kummer distributions. 2019. ⟨hal-02419186v2⟩
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