  A general method to describe stochastic dynamics of Markov processes is
suggested. The method aims to solve three related problems. The determination
of an optimal coordinate for the description of stochastic dynamics. The
reconstruction of time from an ensemble of stochastic trajectories. The
decomposition of stationary stochastic dynamics on eigen-modes which do not
decay exponentially with time. The problems are solved by introducing additive
eigenvectors which are transformed by a stochastic matrix in a simple way -
every component is translated on a constant distance. Such solutions have
peculiar properties. For example, an optimal coordinate for stochastic dynamics
with detailed balance is a multi-valued function. An optimal coordinate for a
random walk on the line corresponds to the conventional eigenvector of the one
dimensional Dirac equation. The equation for the optimal coordinate in a slow
varying potential reduces to the Hamilton-Jacobi equation for the action
function.
