Extrema and Level Crossings of x(2) Processes.
Technical rept. Sep 84-Aug 85,
NORTH CAROLINA UNIV AT CHAPEL HILL CENTER FOR STOCHASTIC PROCESSES
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This document studies the sample path behavior of sq X processes in the neighbourhood of their level crossings and extreme via the development of Slepian model processes. The results, aside from being of particular interest in the study of sq X processes, have a general interest insofar as they indicate which properties of Gaussian processes which has been heavily researched in this regard are mirrored or lost when the assumption of normality is not made. Particular emphasis is placed on the behavior of sq X processes at both high and low levels, these being of considerable practical importance. Also extended are previous results on the asymptotic Poisson form of the point process of high maxima to include also low minima which are in a different domain of attraction thus closing a gap in the theory of 59 sq X processes. Keywords Poisson limit Stochastic processes.
- Statistics and Probability