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07 February 2025
 
  » arxiv » 1508.0099

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Bounds for expected maxima of Gaussian processes and their discrete approximations
Konstantin Borovkov ; Yuliya Mishura ; Alexander Novikov ; Mikhail Zhitlukhin ;
Date 1 Aug 2015
AbstractThe paper deals with the expected maxima of continuous Gaussian processes $X = (X_t)_{tge 0}$ that are H"older continuous in $L_2$-norm and/or satisfy the opposite inequality for the $L_2$-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 $E max_{0le tle 1}X_t$ and investigate the rate of convergence to that quantity of its discrete approximation $E max_{0le ile n}X_{i/n}$. Some further properties of these two maxima are established in the special case of the fractional Brownian motion.
Source arXiv, 1508.0099
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