| Title | Discrete wave-analysis of continuous stochastic processes |
| Authors | Georg Lindgren |
| Alternative Location | http://ida.lub.lu.se/cgi-bi..., Restricted Access |
| Publication | Stochastic Processes and their Applications |
| Year | 1973 |
| Volume | 1 |
| Issue | 1 |
| Pages | 83 - 105 |
| Document type | Article |
| Status | Published |
| Quality controlled | Yes |
| Language | eng |
| Publisher | North-Holland |
| Abstract English | 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. |
| Keywords | stationary processes, crossing problems, wave-length, sampling of continuous processes, maxima of Gaussian processes, |
| ISBN/ISSN/Other | ISSN: 03044149 |
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