UNIFORM QUADRATIC VARIATION FOR GAUSSIAN-PROCESSES

We study the uniform convergence of the quadratic variation of Gaussian processes, taken over large families of curves in the parameter space. A simple application of our main result shows that the quadratic variation of the Brownian sheet along all rays issuing from a point in [0, 1]2 converges uniformly (with probability one) as long as the meshes of the partitions defining the quadratic variation do not decrease too slowly. Another application shows that previous quadratic variation results for Gaussian processes on [0, 1] actually hold uniformly over large classes of partitioning sets.