Possible long-range dependence in fractional random fields. (Q1304351)

The authors outline some elements of \(\alpha\)-generalized random fields. This is a suitable framework to extend Markov diffusion to fractional diffusion. Riesz and Bessel potentials are considered. The general form of the covariance operator of the dual fields is given. The existence of a class of fractional random fields with spectral densities of the form \[ f(\lambda)=c/| \lambda| ^ {2\gamma}(1+| \lambda| ^ 2)^ \alpha, \quad c>0,\;0<\gamma <n,\;\alpha\geq 0,\;\lambda\in {R}^ n, \] is shown.