
Accession Number : AD0729650
Title : Discrete WaveAnalysis of Continuous Stochastic Processes.
Descriptive Note : Research rept.,
Corporate Author : NORTH CAROLINA UNIV CHAPEL HILL DEPT OF STATISTICS
Personal Author(s) : Lindgren,Georg
Report Date : JUN 1971
Pagination or Media Count : 10
Abstract : The behaviour of a continuous time stochastic process in the neighbourhood of zerocrossings and local maxima is compared with the behaviours of a discrete sampled version of the same process. For regular processes, with finite crossingrate or finite rate of local extremes, the behaviour of the sampled version approaches that of the continuous one as the sampling interval tends to zero. Especially the zerocrossing distance and the wavelength (i.e. the time from a local maximum to the next minimum) have asymptotically the same distributions in the discrete and the continuous case. Three numerical illustrations show that there is a good agreement even for rather big sampling intervals. For nonregular processes, with infinite crossingrate, the sampling procedure can yield useful results. An example is given in which a small irregular disturbance is superposed over a regular process. The structure of the regular process is easily observable with a moderate sampling interval, but is completely hidden with a small interval. (Author)
Descriptors : (*STOCHASTIC PROCESSES, SAMPLING), STATISTICAL PROCESSES, PERIODIC VARIATIONS, TIME SERIES ANALYSIS, THEOREMS
Subject Categories : Statistics and Probability
Distribution Statement : APPROVED FOR PUBLIC RELEASE