Consider a diffusion process X=(X_t), with t in [0,1], observed at discrete times and high frequency, solution of a stochastic differential equation whose drift and diffusion coefficients are assumed to be unknown. In this article, we focus on the nonparametric esstimation of the diffusion coefficient. We propose ridge estimators of the square of the diffusion coefficient from discrete observations of X and that are obtained by minimization of the least squares contrast. We prove that the estimators are consistent and derive rates of convergence as the size of the sample paths tends to infinity, and the discretization step of the time interval [0,1] tend to zero. The theoretical results are completed with a numerical study over synthetic data.

翻译：考虑一个扩散过程X=(X_t)，其中t∈[0,1]，在离散时间和高频采样下观测，该过程是漂移系数和扩散系数均未知的随机微分方程的解。本文聚焦于扩散系数的非参数估计。我们基于X的离散观测数据，通过最小化最小二乘对比度，提出了扩散系数平方的岭估计量。我们证明了估计量的一致性，并推导了当样本路径规模趋于无穷大且时间区间[0,1]的离散化步长趋于零时的收敛速率。理论结果辅以合成数据的数值研究。