Asymptotic properties of integral functionals of fractional Brownian fields
Анотація
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.
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