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Article Dans Une Revue Séminaire de Probabilités Année : 2018

Bismut-Elworthy-Li formulae for Bessel processes

Résumé

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.
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Dates et versions

hal-01507054 , version 1 (12-04-2017)

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  • HAL Id : hal-01507054 , version 1

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Henri Elad Altman. Bismut-Elworthy-Li formulae for Bessel processes. Séminaire de Probabilités, 2018, 2215, pp.183--220. ⟨hal-01507054⟩
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