The maximum distribution of a Gaussian stochastic process indexed by a local field

Author:

Evans Steven N.

Abstract

AbstractWe consider continuous Gaussian stochastic process indexed by a compact subset of a vector space over a local field. Under suitable conditions we obtain an asymptotic expression for the probability that such a process will exceed a high level. An important component in the proof of these results is a theorem of independent interest concerning the amount of ‘time’ which the process spends at high levels.

Publisher

Cambridge University Press (CUP)

Subject

General Mathematics,Statistics and Probability

Reference11 articles.

1. Sojourns and Extremes of Stationary Processes

2. Upcrossing probabilities for stationary Gaussian processes

3. Evans S. N. (1986), ‘Sample path properties of Gaussian stochastic processes indexed by a local field’, Proc. London Math. Soc., to appear.

4. Asymptotics of the average number of A-points of overshoot of a Gaussian field beyond a high level;Belyaev;Dokl. Akad. Nauk SSSR,1972

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