This note extends to a broad class of stochastic processes with Gaussian increments the following theorem of R. M. Dudley (Ann. Probability 1 66-103): if $\{\pi_n ...

Let X be a standard Brownian motion. We show that for any locally square integrable function f the quadratic covariation [f(X), X] exists as the usual limit of sums converging in probability. For an ...