Extremes of a certain class of Gaussian processes

We consider the extreme values of fractional Brownian motions, self-similar Gaussian processes and more general Gaussian processes which have a trend -ct[beta] for some constants c,[beta]>0 and a variance t2H. We derive the tail behaviour of these extremes and show that they occur mainly in the neighbourhood of the unique point t0 where the related boundary function (u+ct[beta])/tH is minimal. We consider the case that H<[beta].

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Year of publication:	1999
Authors:	Hüsler, J. ; Piterbarg, V.
Published in:	Stochastic Processes and their Applications. - Elsevier, ISSN 0304-4149. - Vol. 83.1999, 2, p. 257-271
Publisher:	Elsevier
Keywords:	Extreme values Gaussian processes Fractional Brownian motions Self-similar processes

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Type of publication:	Article
Source:	RePEc - Research Papers in Economics

Persistent link: https://www.econbiz.de/10008874557