Extremes of Gaussian Processes

Michael Falk (), Jürg Hüsler () and Rolf-Dieter Reiss ()
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Michael Falk: University of Würzburg, Institute of Mathematics
Jürg Hüsler: University of Berne, Department of Mathematical Statistics and Actuarial Science
Rolf-Dieter Reiss: University of Siegen, Department of Mathematics

Chapter Chapter 10 in Laws of Small Numbers: Extremes and Rare Events, 2011, pp 381-418 from Springer

Abstract: Abstract In this chapter continuous Gaussian processes and their extremes, exceedances and sojourns above a boundary are treated. Results are derived for stationary and locally stationary Gaussian processes. The asymptotic results are then applied to a statistical problem related to empirical characteristic functions. In addition, some results on other non-stationary Gaussian processes are discussed. The relation between the continuous process and its discrete approximation on a certain fine grid is a rather interesting issue, in particular for simulations or approximations.

Keywords: Brownian Motion; Gaussian Process; Fractional Brownian Motion; Large Deviation Principle; Hurst Parameter (search for similar items in EconPapers)
Date: 2011
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-0348-0009-9_10

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DOI: 10.1007/978-3-0348-0009-9_10

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