Discrete waveanalysis of continuous stochastic processes
(1973) In Stochastic Processes and their Applications 1(1). p.83105 Abstract
 he behaviour of a continuoustime stochastic process in the neighbourhood of zerocrossings and local maxima is compared with the behaviour 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,... (More)
 he behaviour of a continuoustime stochastic process in the neighbourhood of zerocrossings and local maxima is compared with the behaviour 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. (Less)
Please use this url to cite or link to this publication:
https://lup.lub.lu.se/record/1273136
 author
 Lindgren, Georg ^{LU}
 organization
 publishing date
 1973
 type
 Contribution to journal
 publication status
 published
 subject
 keywords
 stationary processes, crossing problems, wavelength, sampling of continuous processes, maxima of Gaussian processes
 in
 Stochastic Processes and their Applications
 volume
 1
 issue
 1
 pages
 83  105
 publisher
 Elsevier
 external identifiers

 scopus:0041923820
 ISSN
 1879209X
 language
 English
 LU publication?
 yes
 id
 b6333de1b6c74fad893f5e0bcc4e453b (old id 1273136)
 alternative location
 http://ida.lub.lu.se/cgibin/elsevier_local?YMT00110A03044149V0001I0173900343
 date added to LUP
 20160401 15:38:42
 date last changed
 20210103 04:54:28
@article{b6333de1b6c74fad893f5e0bcc4e453b, abstract = {{he behaviour of a continuoustime stochastic process in the neighbourhood of zerocrossings and local maxima is compared with the behaviour 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 = {{Lindgren, Georg}}, issn = {{1879209X}}, keywords = {{stationary processes; crossing problems; wavelength; sampling of continuous processes; maxima of Gaussian processes}}, language = {{eng}}, number = {{1}}, pages = {{83105}}, publisher = {{Elsevier}}, series = {{Stochastic Processes and their Applications}}, title = {{Discrete waveanalysis of continuous stochastic processes}}, url = {{http://ida.lub.lu.se/cgibin/elsevier_local?YMT00110A03044149V0001I0173900343}}, volume = {{1}}, year = {{1973}}, }