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A functional limit theorem for the integrals over level sets of a Gaussian random field. (English. Russian original) Zbl 1334.60046
Theory Probab. Appl. 60, No. 1, 150-161 (2016); translation from Teor. Veroyatn. Primen. 60, No. 1, 186-198 (2015).
MSC:
60F17 Functional limit theorems; invariance principles
60F05 Central limit and other weak theorems
60G60 Random fields
60G15 Gaussian processes
60G57 Random measures
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References:
[1] R. J. Adler and J. E. Taylor, Random Fields and Geometry, Springer, New York, 2007.
[2] J.-M. Azaï s and M. Wschebor, Level Sets and Extrema of Random Processes and Fields, Wiley, Hoboken, NJ, 2009.
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[11] D. Meschenmoser and A. Shashkin, Functional central limit theorem for the measures of level surfaces of the Gaussian random field, Theory Probab. Appl., 57 (2013), pp. 162–172. · Zbl 1278.60052
[12] A. Shashkin, A functional central limit theorem for the level measure of a Gaussian random field, Statist. Probab. Lett., 83 (2013), pp. 637–643. · Zbl 1266.60061
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