  Atomistic simulations with methods such as molecular dynamics are extremely
powerful tools to understand nanoscale dynamical behavior. The resulting
trajectories, by the virtue of being embedded in a high-dimensional
configuration space, can however be difficult to analyze and interpret. This
makes low-dimensional representations, especially in terms of discrete jump
processes, extremely valuable. This simplicity however usually comes at the
cost of accuracy, as tractable representations often entail simplifying
assumptions that are not guaranteed to be realized in practice. In this paper,
we describe a discretization scheme for continuous trajectories that enables an
arbitrarily accurate representation in terms of a Markov Renewal Process over a
discrete state space. The accuracy of the model converges exponentially fast as
a function of a continuous parameter that has the interpretation of a local
correlation time of the dynamics.
