  We introduce a new nonparametric density estimator inspired by Markov Chains,
and generalizing the well-known Kernel Density Estimator (KDE). Our estimator
presents several benefits with respect to the usual ones and can be used
straightforwardly as a foundation in all density-based algorithms. We prove the
consistency of our estimator and we find it typically outperforms KDE in
situations of large sample size and high dimensionality. We also employ our
density estimator to build a local outlier detector, showing very promising
results when applied to some realistic datasets.
