Non parametric estimation of the jump coefficient of a diffusion with jumps

Schmisser, Émeline

Document type :

Pré-publication ou Document de travail

Title :

Non parametric estimation of the jump coefficient of a diffusion with jumps

Author(s) :

Schmisser, Émeline [Auteur]
Université de Lille
Laboratoire Paul Painlevé - UMR 8524 [LPP]

English keyword(s) :

jump diffusions
nonparametric estimation
model selection 62G05
62M05

HAL domain(s) :

Mathématiques [math]/Statistiques [math.ST]

English abstract : [en]

In this article, we consider a jump diffusion process (Xt) t≥0 with drift function b, diffusion coefficient σ and jump coefficient ξ. This process is supposed to be ergodic, exponentially βmixing and stationary. It is ...
Show more >In this article, we consider a jump diffusion process (Xt) t≥0 with drift function b, diffusion coefficient σ and jump coefficient ξ. This process is supposed to be ergodic, exponentially βmixing and stationary. It is observed at discrete times t = 0, ∆,. .. , n∆. The sampling interval ∆ tends to 0 and the time interval n∆ tends to infinity. We construct a robust, adaptive non-parametric estimator of the function ξ 4 thanks to a penalized least-square approach. We provide bounds of the empirical and L 2-risk of our estimator.Show less >

Language :

Anglais

Collections :

Laboratoire Paul Painlevé - UMR 8524

Source :

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