Accession Number : AD0729650

Title :   Discrete Wave-Analysis 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 zero-crossings and local maxima is compared with the behaviours of a discrete sampled version of the same process. For regular processes, with finite crossing-rate 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 zero-crossing distance and the wave-length (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 non-regular processes, with infinite crossing-rate, 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