On superior limits for the increments of Gaussian processes

Kyo Shin Huang, Yong Kab Choi and Jong Soo Jung

Statistics & Probability Letters, 1997, vol. 35, issue 3, 289-296

Abstract: 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]2

Keywords: Wiener; process; Gaussian; process; Law; of; large; numbers; Law; of; iterated; logarithm; Regularly; varying; function; and; Borel-Cantelli; lemma (search for similar items in EconPapers)
Date: 1997
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