UNIFORM QUADRATIC VARIATION FOR GAUSSIAN-PROCESSES

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