Extremes of Gaussian processes with a smooth random variance

Jörg Hösler, Vladimir Piterbarg and Ekaterina Rumyantseva

Stochastic Processes and their Applications, 2011, vol. 121, issue 11, 2592-2605

Abstract: Let ξ(t) be a standard stationary Gaussian process with covariance function r(t), and η(t), another smooth random process. We consider the probabilities of exceedances of ξ(t)η(t) above a high level u occurring in an interval [0,T] with T>0. We present asymptotically exact results for the probability of such events under certain smoothness conditions of this process ξ(t)η(t), which is called the random variance process. We derive also a large deviation result for a general class of conditional Gaussian processes X(t) given a random element Y.

Keywords: Gaussian; process; Conditional; Gaussian; process; Locally; stationary; Ruin; probability; Random; variance; Extremes; Large; deviations; Fractional; Brownian; motion (search for similar items in EconPapers)
Date: 2011
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (4)

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