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Discrete wave-analysis of continuous stochastic processes

Lindgren, Georg LU (1973) In Stochastic Processes and their Applications 1(1). p.83-105
Abstract
he 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,... (More)
he 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. (Less)
Please use this url to cite or link to this publication:
author
organization
publishing date
type
Contribution to journal
publication status
published
subject
keywords
stationary processes, crossing problems, wave-length, 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
1879-209X
language
English
LU publication?
yes
id
b6333de1-b6c7-4fad-893f-5e0bcc4e453b (old id 1273136)
alternative location
http://ida.lub.lu.se/cgi-bin/elsevier_local?YMT00110-A-03044149-V0001I01-73900343
date added to LUP
2009-06-03 17:01:30
date last changed
2017-03-15 13:26:59
@article{b6333de1-b6c7-4fad-893f-5e0bcc4e453b,
  abstract     = {he 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.},
  author       = {Lindgren, Georg},
  issn         = {1879-209X},
  keyword      = {stationary processes,crossing problems,wave-length,sampling of continuous processes,maxima of Gaussian processes},
  language     = {eng},
  number       = {1},
  pages        = {83--105},
  publisher    = {Elsevier},
  series       = {Stochastic Processes and their Applications},
  title        = {Discrete wave-analysis of continuous stochastic processes},
  volume       = {1},
  year         = {1973},
}