In:
Communications on Pure and Applied Mathematics, Wiley, Vol. 44, No. 8-9 ( 1991-10), p. 925-938
Abstract:
Let X ( t ), t ≧ 0, be a real stationary Gaussian process, and, for u 〉 0 and t 〉 0, let L t ( u ) be the time spent by X ( s ), 0 ≦ s ≦ t , above the level u . Here u is taken to be a function u ( t ) of t , and L t is defined as L t ( u ( t )). It is shown that the distribution of ( L t – EL t )/(Var L t ) 1/2 converges, for t → ∞ and u ( t ) → ∞, to a standard normal distribution under various conditions relating the growth of u ( t ) to the decay of the covariance and other functions associated with it.
Type of Medium:
Online Resource
ISSN:
0010-3640
,
1097-0312
DOI:
10.1002/cpa.3160440807
Language:
English
Publisher:
Wiley
Publication Date:
1991
detail.hit.zdb_id:
1468142-0
detail.hit.zdb_id:
1568-4
detail.hit.zdb_id:
220318-2
SSG:
17,1
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