Extremes of Gaussian processes with a smooth random variance
Let Î¾(t) be a standard stationary Gaussian process with covariance function r(t), and Î·(t), another smooth random process. We consider the probabilities of exceedances of Î¾(t)Î·(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 Î¾(t)Î·(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.
Volume (Year): 121 (2011)
Issue (Month): 11 (November)
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