  A deterministic walk in a random environment can be understood as a general
random process with finite-range dependence that starts repeating a loop once
it reaches a site it has visited before. Such process lacks the Markov
property. We study the exponential decay of the probabilities that the walk
will reach sites located far away from the origin. We also study a similar
problem for the continuous analogue: the process that is a solution to an ODE
with random coefficients. In this second model the environment also has
"teleports" which are the regions from where the process can make discontinuous
jumps.
