Non-parametric adaptive estimation of the drift for a jump diffusion process

Emeline Schmisser (1)

1 LPP - Laboratoire Paul Painlevé - UMR 8524

In this article, we consider a jump diffusion process (X_t)observed at discrete times t=0,Delta,...,nDelta. The sampling interval Delta tends to 0 and nDelta tends to infinity. We assume that (X_t) is ergodic, strictly stationary and exponentially \beta-mixing. We use a penalized least-square approach to compute two adaptive estimators of the drift function b. We provide bounds for the risks of the two estimators.

Mots clés: jump diffusion; drift estimation

Domaines: Statistiques [math.ST]; Théorie [stat.TH]

Emeline Schmisser. Non-parametric adaptive estimation of the drift for a jump diffusion process. Stochastic Processes and their Applications, 2014, 124 (1), pp.883-914. ⟨10.1016/j.spa.2013.09.012⟩. ⟨hal-00704637v3⟩