Non parametric estimation of the diffusion coefficents of a diffusion with jumps
Statistics Theory
2013-11-27 v2 Statistics Theory
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 sigma^2+xi^2 and sigma^2. We provide bounds for the risks of the two estimators.
Keywords
Cite
@article{arxiv.1311.6435,
title = {Non parametric estimation of the diffusion coefficents of a diffusion with jumps},
author = {Emeline Schmisser},
journal= {arXiv preprint arXiv:1311.6435},
year = {2013}
}