In this paper we examine the issue of characterizing the transport associated with gravitational instabilities in relatively cold discs , discussing in particular under which condition it can be described within a local , viscous framework .
We present the results of global , three-dimensional , SPH simulations of self-gravitating accretion discs , in which the disc is cooled using a simple parameterization for the cooling function .
Our simulations show that the disc settles in a “ self-regulated ” state , where the axisymmetric stability parameter Q \approx 1 and where transport and energy dissipation are dominated by self-gravity .
We have computed the gravitational stress tensor and compared our results with expectations based on a local theory of transport .
We find that , for disc masses smaller than 0.25 M _ { \star } 
and aspect ratio H / r < 0.1 , transport is determined locally , thus allowing for a viscous treatment of the disc evolution .