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We analyze a stochastic version of the so-called diffusionvelocity method. For moving particles with velocities depending on the gradient of their density function we introduce a stochastic scheme based on the simulation of the gradient process where the values of the density are recovered by a numerical integration method. We apply this method to the diffusion equation and show a convergence result.

Mathematics Subject Classification (2010): 65C20, 68U20, 65M06.

Keywords: Stochastic simulation, diffusion, gradient process.