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Non parametric estimation of the diffusion coefficents of a diffusion with jumps (1311.6435v2)
Published 25 Nov 2013 in math.ST and stat.TH
Abstract: In this article, we consider a jump diffusion process (X_t), with drift function b, diffusion coefficient sigma and jump coefficient xi{2}. This process is 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 adaptive estimators of the functions sigma2+xi2 and sigma2. We provide bounds for the risks of the two estimators.