Spectral conditions for sojourn and extreme value limit theorems for Gaussian processes

Simeon M. Berman

Stochastic Processes and their Applications, 1991, vol. 39, issue 2, 201-220

Abstract: Let X(t), t[greater-or-equal, slanted]0, be a stationary Gaussian process, and define the sojourn time Lu(t)=mes{s:0 [less-than-or-equals, slant]s[less-than-or-equals, slant]t,X(s)>u} and the maximum Z(t)=max(X(s): 0 [less-than-or-equals, slant]0[less-than-or-equals, slant]s[less-than-or-equals, slant]t). Limit theorems for the distributions of Lu(t) and Z(t), for t, u --> [infinity], are obtained under specified conditions on the spectral density of the process. The results supplement earlier theorems obtained under suitable conditions on the covariance function.

Keywords: stationary; Gaussian; processes; spectral; density; function; mixing; condition; sojourn; above; a; level; extreme; value (search for similar items in EconPapers)
Date: 1991
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