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The authors propose a general framework for designing new MCMC samplers, including methods that use stochastic gradients. Their approach is to define a stochastic dynamical system whose stationary distribution is the target distribution from which we want to sample from. The stochastic dynamical system is represented through a stochastic differential equation that is simulated through an epsilon-discretization approach. As the step-size parameter epsilon goes to zero, the bias in the simulation vanishes. The proposed approach can handle stochastic approximations obtained by sub-sampling the data in mini-batches.