Discrete Wave-Analysis of Continuous Stochastic Processes.
NORTH CAROLINA UNIV CHAPEL HILL DEPT OF STATISTICS
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The behaviour of a continuous time stochastic process in the neighbourhood of zero-crossings and local maxima is compared with the behaviours 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
- Statistics and Probability