Uniform Hölder exponent of a stationary increments Gaussian process: Estimation starting from average values

Let {X(t)}t∈R be a stationary increments Gaussian process satisfying some assumptions. By using the notion of generalized quadratic variation we build a strongly consistent and asymptotically normal estimator of the uniform Hölder exponent of X, over a compact interval. Our estimator is obtained starting from average values of the process over a regular grid.