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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Submitted on : Tuesday, December 6, 2016 - 8:27:30 PM
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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. 2016. ⟨hal-01410989v1⟩

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