On superior limits for the increments of Gaussian processes

Let {X(t); t [greater-or-equal, slanted] 0} be a Gaussian process with stationary increments E{X(t + s) - X(t)}2 = [sigma]2(s). Let at(t [greater-or-equal, slanted] 0) be a nondecreasing function of t with 0 [infinity] {(tk+1 - tk)/atk} [infinity] {(tk+1 - tk)/atk} [greater-or-equal, slanted] 1, then we have a value [delta] almost surely, where [delta]=inf{[gamma]>;[summation operator](tk(log(n)tk)/atk)-[gamma]2Wiener process Gaussian process Law of large numbers Law of iterated logarithm Regularly varying function and Borel-Cantelli lemma