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Asymptotics in small time for the density of a stochastic differential equation driven by a stable LEVY process

Abstract : This work focuses on the asymptotic behavior of the density in small time of a stochastic differential equation driven by an α-stable process with index α ∈ (0, 2). We assume that the process depends on a parameter β = (θ, σ) T and we study the sensitivity of the density with respect to this parameter. This extends the results of [5] which was restricted to the index α ∈ (1, 2) and considered only the sensitivity with respect to the drift coefficient. By using Malliavin calculus, we obtain the representation of the density and its derivative as an expectation and a conditional expectation. This permits to analyze the asymptotic behavior in small time of the density, using the time rescaling property of the stable process. MSC2010: 60G51; 60G52; 60H07; 60H20; 60H10; 60J75.
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https://hal.archives-ouvertes.fr/hal-01410989
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Submitted on : Wednesday, November 8, 2017 - 4:20:54 PM
Last modification on : Tuesday, March 8, 2022 - 12:32:02 PM
Long-term archiving on: : Friday, February 9, 2018 - 2:09:35 PM

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  • HAL Id : hal-01410989, version 2

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Emmanuelle Clément, Arnaud Gloter, Huong Nguyen. Asymptotics in small time for the density of a stochastic differential equation driven by a stable LEVY process. 2017. ⟨hal-01410989v2⟩

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