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

In this article, we consider a jump diffusion process (X-t)(t >= 0) observed at discrete times t = 0, Delta, ..., n Delta. The sampling interval Delta tends to 0 and n Delta tends to infinity. We assume that (X-t)(t >= 0) is ergodic, strictly stationary and exponentially beta-mixing. We use a penalised least-square approach to compute two adaptive estimators of the drift function b. We provide bounds for the risks of the two estimators. (C) 2013 Elsevier B.V. All rights reserved.