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:
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, 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
- 2016-04-01 15:38:42
- date last changed
- 2021-01-03 04:54:28
@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}},
keywords = {{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}},
url = {{http://ida.lub.lu.se/cgi-bin/elsevier_local?YMT00110-A-03044149-V0001I01-73900343}},
volume = {{1}},
year = {{1973}},
}