Theory of Probability and Mathematical Statistics
Asymptotic properties of integral functionals of fractional Brownian fields
V. I. Makogin
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Abstract: Two theorems describing the asymptotic behavior of integral functionals of multidimensional self-similar random fields are proved. For a d-dimensional fractional Brownian field depending on N parameters, a theorem on the convergence of the integral mean-type functional is established. The weak convergence of an integral functional of a d-dimensional anisotropic self-similar random field with N parameters to the local time is proved under the assumption that the continuous local time exists for this field.
Keywords: Local time, self-similar fields, anisotropic fractional Brownian field
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