Accession Number : AD0262736

Title :   ON THE STRICTLY STATIONARY PROCESS WITH ADDITIVE SPECTRUM

Corporate Author : COLUMBIA UNIV NEW YORK

Personal Author(s) : MARUYAMA,GISIRO

Report Date : 30 AUG 1961

Pagination or Media Count : 31

Abstract : Suppose X(t), - < t < , is a real-valued weakly stationary process of the second order, i.e., X(t) has the second moment and (h) = E(X(t+h)X(t)) = cos h dS( ), m = E(X(t)) are independent o t, then X(t) has the spectral resolution X(t) = ei t dZ( ) = (cos td ( )+ sin td ( )), with obvious notations. If further X(t) is Gaussian, then ( ( ), 0 < ) and ( ( ), 0 < ) are independent and identically distributed Gaussian processes with independent increments. By ( ( ), ( ), 0 < ) is denoted a two-dimensional process with independent increments (additive process), i.e., any number of increments ( ( k+1) - ( k), ( k+1) - ( k)), 1 k n, are independent if 0 1 2... n+1. (Author)

Descriptors :   *STATISTICAL PROCESSES, FUNCTIONAL ANALYSIS, INTEGRAL EQUATIONS

Distribution Statement : APPROVED FOR PUBLIC RELEASE