  Several stochastic processes modeling molecular motors on a linear track are
given by random walks (not necessarily Markovian) on quasi 1d lattices and
share a common regenerative structure. Analyzing this abstract common
structure, we derive information on the large fluctuations of the stochastic
process by proving large deviation principles for the first--passage times and
for the position. We focus our attention on the Gallavotti-Cohen-type symmetry
of the position rate function (fluctuation theorem), showing its equivalence
with the independence of suitable random variables. In the special case of
Markov random walks, we show that this symmetry is universal only inside a
suitable class of quasi 1d lattices.
