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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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Dates and versions

hal-01410989 , version 1 (06-12-2016)
hal-01410989 , version 2 (08-11-2017)

Identifiers

  • HAL Id : hal-01410989 , version 2

Cite

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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