Probability tails of Gaussian extrema

Gennady Samorodnitsky

Stochastic Processes and their Applications, 1991, vol. 38, issue 1, 55-84

Abstract: We study the supremum of 'the' standard isonormal linear process L on a subset of a real Hilbert space H. Upper and lower bounds on the probability that supx[epsilon] LX>[lambda], [lambda] large, are found. We treat a number of examples. These include the distribution of the maximum of certain 'locally stationary' processes on 1, as well as those of the rectangle indexed, pinned Brownian sheet in k and the half-plane indexed pinned sheet in 2. We also consider Brownian motion indexed by convex sets in [0, 1]2.

Keywords: Gaussian; processes; isonormal; process; supremum; metric; entropy; Brownian; sheet; empirical; process (search for similar items in EconPapers)
Date: 1991
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Citations: View citations in EconPapers (9)

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