  We define and study the multiparameter fractional Brownian motion. This
process is a generalization of both the classical fractional Brownian motion
and the multiparameter Brownian motion, when the condition of independence is
relaxed. Relations with the L\'evy fractional Brownian motion and with the
fractional Brownian sheet are discussed. Different notions of stationarity of
the increments for a multiparameter process are studied and applied to the
fractional property. Using self-similarity we present a characterization for
such processes. Finally, behavior of the multiparameter fractional Brownian
motion along increasing paths is analysed.
