Functional limits of empirical distributions in crossing theory

We present a functional limit theorem for the empirical level-crossing behaviour of a stationary Gaussian process. This leads to the well-known Slepian model process for a Gaussian process after an upcrossing of a prescribed level as a weak limit in C-space for an empirically defined finite set of functions. We also stress the importance of choosing a suitable topology by giving some natural examples of continuous and non-continuous functionals.

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Year of publication:	1977
Authors:	Lindgren, Georg
Published in:	Stochastic Processes and their Applications. - Elsevier, ISSN 0304-4149. - Vol. 5.1977, 2, p. 143-149
Publisher:	Elsevier
Keywords:	functional limit theorem empirical process stationary normal process level crossing

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Type of publication:	Article
Source:	RePEc - Research Papers in Economics

Persistent link: https://www.econbiz.de/10008874706