J Austral Math Soc Ser A 46 pp69--87, 1989.

The Maximum Distribution of a Gaussian Stochastic Process Indexed by a Local Field

Steven N. Evans

(Received 24 November 1986; revised 3 July 1987)

Abstract

We consider continuous Gausiian 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.

1980 AMS Subject Classification (1985 Revision): 60G15, 60G10, 26E30

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Authors

Steven N. Evans: Department of Mathematics, University of Virginia, Mathematics-Astronomy Building, Charlottesville, Virginia 22903, U.S.A.

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Last Modified: Wed Feb 19 10:27:50 2003