Bounds for expected maxima of Gaussian processes and their discrete approximations

Taylor & Francis
Publication Type:
Journal Article
Stochastics: An International Journal of Probability and Stochastic Processes, 2017, 89 (1), pp. 21 - 37
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© 2015 Taylor & Francis The paper deals with the expected maxima of continuous Gaussian processes (Formula presented.) that are Hölder continuous in (Formula presented.)-norm and/or satisfy the opposite inequality for the (Formula presented.)-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 (Formula presented.) and investigate the rate of convergence to that quantity of its discrete approximation (Formula presented.). Some further properties of these two maxima are established in the special case of the fractional Brownian motion.
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