Abstract
In this paper we analyze sufficient conditions to guarantee the differentiability under the integral sign of a certain class of random upper semicontinuous functions depending on a real-valued parameter. Several concepts of differential for this mappings are considered: the Fréchet differentiability of the support function, the π-differentiability, the De Blasi differentiability, and thes-differentiability.
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Rodríguez-Muñiz, L.J., López-Díaz, M. & Ángeles Gil, M. Differentiating random upper semicontinuous functions under the integral sign. Test 12, 241–258 (2003). https://doi.org/10.1007/BF02595821
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DOI: https://doi.org/10.1007/BF02595821