Bounds for expected maxima of Gaussian processes and their discrete approximations. Issue 1 (2nd January 2017)

• Record Type: Journal Article
• Authors: Borovkov, Konstantin; Mishura, Yuliya; Novikov, Alexander; Zhitlukhin, Mikhail
• Is Part Of: Stochastics. Volume 89:Issue 1(2017)
• Page Start: 21
• Page End: 37
• Publication Date: 2017-01-02
• Subjects: Expected maximum -- Gaussian processes -- fractional Brownian motion -- discrete approximation -- processes with long memory; 60G15 -- 60G22 -- 60J65; Stochastic processes -- Periodicals; Probabilities -- Periodicals; 519.2
• DOI: 10.1080/17442508.2015.1126282
• Languages: English
• ISSNs: 1744-2508

Abstract

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.