Abstract
In this paper, a useful and suitable form of the second moment of the Euler characteristic (EC) of excursion sets of a random field with respect to a special threshold is presented, which can be used in numerical evaluations of the variance of EC. We also present an extension to the higher moments of EC. Finally, a new method of simulating is presented and the results are compared with the three older well known methods of simulation based on the moment estimation and monte carlo idea.
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