 Discrete wave-analysis of continuous stochastic processesGeorg Lindgren Stochastic Processes and their Applications, 1973, vol. 1, issue 1, 83-105 Abstract: The behaviour of a continuous-time stochastic process in the neighbourhood of zero-crossings and local maxima is compared with the behaviour 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. Keywords: stationary; processes; crossing; problems; wave-length; sampling; of; continuous; processes; maxima; of; Gaussian; processes (search for similar items in EconPapers) Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:eee:spapps:v:1:y:1973:i:1:p:83-105 Ordering information: This journal article can be ordered from Access Statistics for this article Stochastic Processes and their Applications is currently edited by T. Mikosch More articles in Stochastic Processes and their Applications from Elsevier |
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