# Accession Number:

## ADA218338

# Title:

## Slepian Models and Regression Approximations in Crossing and Extreme Value Theory

# Descriptive Note:

## Technical rept.

# Corporate Author:

## NORTH CAROLINA UNIV AT CHAPEL HILL CENTER FOR STOCHASTIC PROCESSES

# Personal Author(s):

# Report Date:

## 1990-01-01

# Pagination or Media Count:

## 54.0

# Abstract:

In crossing theory for stochastic processes the distribution of quantities such as distances between level crossing, maximum height of an excursion between level crossing, amplitude and wavelength, etc., can only be written in the form of infinite dimensional integrals, which are difficult to evaluate numerically. A Slepian model is an explicit random function representation of the process after a level crossing and it consists of one regression term and one residual process. The regression approximation of a crossing variable is defined as the corresponding variable in the regression term of the Slepian model, and its distribution can be evaluated numerically as a finite-dimensional integral. This paper reviews the use and structure of the Slepian model the regression method and shows how they can be used to obtain good numerical approximations to various crossing variables. It gives a detailed account of the regression method for Gaussian processes with auxilliary variables chosen in a recursive way.

# Descriptors:

# Subject Categories:

- Statistics and Probability