Distribution of the Maximum of a Gaussian Process by Monte Carlo.
Technical rept. 1 Sep 85-30 Sep 86,
NORTH CAROLINA UNIV AT CHAPEL HILL CENTER FOR STOCHASTIC PROCESSES
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First a simple practical procedure for approximating a stationary Gaussian process over a finite interval by a trigonometric polynomial with predetermined error is described. The approximation is then used to calculate the distribution of the maximum, using a novel Monte Carlo method with a control variable which drastically reduces the variance. Finally, the outlined approach is compared to the moving-average technique and shown to be superior for continuous-time, narrow-band processes.
- Statistics and Probability