Possible long-range dependence in fractional random fields

Many existing stochastic models have been developed for description and analysis of Markov diffusion. This paper outlines the new concept of a-duality which lays the foundation for an extension of Markov diffusion to fractional diffusion. The theory of Riesz and Bessel potentials and the corresponding potential spaces play a key role in this new approach. We establish the existence of an important subclass of fractional random fields, namely that of fractional Riesz-Bessel motions, which extends the class of fractional Brownian motions. Asa result, the scope of Markov diffusion is widened to cover random fields with long-range dependence. (C) 1999 Elsevier Science B.V. All rights reserved.