  We develop a novel class of MCMC algorithms based on a stochastized Nesterov
scheme. With an appropriate addition of noise, the result is a
time-inhomogeneous underdamped Langevin equation, which we prove emits a
specified target distribution as its invariant measure. Convergence rates to
stationarity under Wasserstein-2 distance are established as well.
Metropolis-adjusted and stochastic gradient versions of the proposed Langevin
dynamics are also provided. Experimental illustrations show superior
performance of the proposed method over typical Langevin samplers for different
models in statistics and image processing including better mixing of the
resulting Markov chains.
