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Properties of local-nondeterminism of Gaussian and stable random fields and their applications. (English) Zbl 1128.60041
The author reviews various forms of local nondeterminism and sectorial local nondeterminism of random processes and fields. Gaussian and stable cases are considered. Sufficient spectral conditions for Gaussian random fields with stationary increments to be strongly locally nondeterministic are given. The author shows some applications in studying the law of the iterated logarithm, Hausdorff dimension and Hausdorff measure of sample paths, loacal times and level sets of Gaussian random fields.
MSC:
60G60Random fields
60G17Sample path properties