Abstract. Electrostatic turbulence and associated convective transport at the edge of a tokamak plasma are strongly modified in a layer of stochastic magnetic field lines. Experimental observations during ergodic divertor operation show a decrease of density fluctuations but no evidence of a change of the turbulent cross field diffusivity. In this paper, the underlying mechanisms are studied using 3D numerical simulations of flux driven resistive ballooning turbulence. Three key elements are found to determine transport due to fluctuations in the stochastic layer: First, steady state eddies appear due to modified equilibrium pressure and potential. Second, large scale pressure fluctuations decrease but small scale velocity fluctuations tend to increase. Third, the poloidal plasma rotation is suppressed and zonal flows are reduced by an anomalous friction. In total, the convective flux is not quenched by the magnetic field perturbation. The impact of stochastic field lines on electrostatic turbulence is of interest for many experimental situations such as the stochastic boundary of stellarators and transport in the vicinity of the separatrix of standard tokamak divertors.