Accession Number : ADA194569

Title :   Limiting Distributions of Non-Linear Vector Functions of Stationary Gaussian Processes.

Descriptive Note : Technical rept. Sep 87-Aug 88,

Corporate Author : NORTH CAROLINA UNIV AT CHAPEL HILL CENTER FOR STOCHASTIC PROCESSES

Personal Author(s) : Ho, Hwai-Chung ; Sun, Tze-Chien

PDF Url : ADA194569

Report Date : Mar 1988

Pagination or Media Count : 21

Abstract : Given a stationary Gaussian vector process x sub m, ym an element of Z, and two real functions H(x) and K(x) we define Z sub H superscript N define Sum from m=1 to (n-1) of Inverse A sub n Sum from m=1 to (n-1) of Sub m and Sub K superscript k Inverse B Sub n Sum from m=1 to (n-1) of Sub n where An and Bn are some appropriate constants. The joint limiting distribution of Sub H superscript n Sub k superscript k is investigated. It is shown that Sub H superscript n and Sub k superscript k are asymptotically independent when one of them satisfies a central limit theorem. The application of this to the limiting distribution for a certain class of non-linear infinite-coordinated functions of a Gaussian process is also discussed. Keywords: Central limit theorem; Nin-central limit theorem; Long range dependence; Stationary Gaussian vector processes.

Descriptors :   *STATISTICAL PROCESSES, *VECTOR ANALYSIS, DISTRIBUTION, LIMITATIONS, LONG RANGE(DISTANCE), LONG RANGE(TIME), NONLINEAR SYSTEMS, STATIONARY, THEOREMS

Subject Categories : Statistics and Probability

Distribution Statement : APPROVED FOR PUBLIC RELEASE