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Pré-Publication, Document De Travail Année : 2015

LAN property for stochastic differential equations with additive fractional noise and continuous time observation

Résumé

We consider a stochastic differential equation with additive fractional noise of Hurst parameter H > 1/2, and a non-linear drift depending on an unknown parameter. We show the Local Asymptotic Normality property (LAN) of this parametric model with rate √ τ as τ → ∞, when the solution is observed continuously on the time interval [0, τ ]. The proof uses ergodic properties of the equation and a Poincaré type inequality.
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Dates et versions

hal-01241749 , version 1 (10-12-2015)

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  • HAL Id : hal-01241749 , version 1

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Eulalia Nualart, Samy Tindel. LAN property for stochastic differential equations with additive fractional noise and continuous time observation. 2015. ⟨hal-01241749⟩
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