Abstract
The paper deals with the expected maxima of continuous Gaussian processes that are Hölder continuous in
-norm and/or satisfy the opposite inequality for the
-norms of their increments. Examples of such processes include the fractional Brownian motion and some of its “relatives” (of which several examples are given in the paper). We establish upper and lower bounds for
and investigate the rate of convergence to that quantity of its discrete approximation
. Some further properties of these two maxima are established in the special case of the fractional Brownian motion.
Acknowledgements
The last author is grateful to V.I. Piterbarg for interesting discussions of the topic of the paper. We are grateful to the anonymous referee for her/his useful remarks that helped to improve the paper.
Notes
No potential conflict of interest was reported by the authors.
Dedicated to Bernt Øksendal on occasion of his 70th birthday.