ON THE STRICTLY STATIONARY PROCESS WITH ADDITIVE SPECTRUM
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)
Document Details
- Document Type
- Technical Report
- Publication Date
- Aug 30, 1961
- Accession Number
- AD0262736
Entities
People
- Gisiro Maruyama
Organizations
- Columbia University