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ON THE FIRST HITTING TIMES FOR ONE-DIMENSIONAL ELLIPTIC DIFFUSIONS

Abstract : In this article, we obtain properties of the law associated to the first hitting time of a threshold by a one-dimensional uniformly elliptic diffusion process and to the associated process stopped at the threshold. Our methodology relies on the parametrix method that we apply to the associated Markov semigroup. It allows to obtain explicit expressions for the corresponding transition densities and to study its regularity properties up to the boundary under mild assumptions on the coefficients. As a by product, we also provide Gaussian upper estimates for these laws and derive a probabilistic representation that may be useful for the construction of an unbiased Monte Carlo path simulation method, among other applications.
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https://hal.archives-ouvertes.fr/hal-01373940
Contributor : Noufel Frikha <>
Submitted on : Thursday, September 29, 2016 - 2:17:16 PM
Last modification on : Friday, March 27, 2020 - 3:13:38 AM
Document(s) archivé(s) le : Friday, December 30, 2016 - 1:55:48 PM

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  • HAL Id : hal-01373940, version 1

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Noufel Frikha, Arturo Kohatsu-Higa, Libo Li. ON THE FIRST HITTING TIMES FOR ONE-DIMENSIONAL ELLIPTIC DIFFUSIONS. 2016. ⟨hal-01373940⟩

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