  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.
