Bismut-Elworthy-Li formulae for Bessel processes

Abstract : In this article we are interested in the differentiability property of the Markovian semi-group corresponding to the Bessel processes of nonnegative dimension. More precisely, for all δ ≥ 0 and T > 0, we compute the derivative of the function x → P δ T F (x), where (P δ t) t≥0 is the transition semi-group associated to the δ-dimensional Bessel process, and F is any bounded Borel function on R +. The obtained expression shows a nice interplay between the transition semi-groups of the δ-and the (δ + 2)-dimensional Bessel processes. As a consequence, we deduce that the Bessel processes satisfy the strong Feller property, with a continuity modulus which is independent of the dimension. Moreover, we provide a probabilistic interpretation of this expression as a Bismut-Elworthy-Li formula.
Type de document :
Pré-publication, Document de travail
2017
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https://hal.archives-ouvertes.fr/hal-01507054
Contributeur : Henri Elad Altman <>
Soumis le : mercredi 12 avril 2017 - 14:45:09
Dernière modification le : mercredi 19 avril 2017 - 11:12:28

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  • HAL Id : hal-01507054, version 1

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INSMI | UPMC | USPC | PMA

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Henri Elad Altman. Bismut-Elworthy-Li formulae for Bessel processes. 2017. <hal-01507054>

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