Large deviations for a random walk in dynamical random environment

We consider a random walk X-t epsilon Z(d), t epsilon Z(+), in a dynamical random environment (xi(t)(x), x epsilon Z(d)), t epsilon Z(+), with a mutual interaction with each other. The Markov process (X-t, xi(t) (x), x epsilon Z(d)) is a perturbation of a process for which the random walk X-t and the environment xi(t)(x), x epsilon Z(d) are independent, X-t, t epsilon Z(+) is a homogeneous random walk in Z(d) and the environment xi(t)(x), x epsilon Z(d) behaves independently in each site as an ergodic Markov chain. For the perturbated process we assume that 1. The interaction between the position of the particle and the environment is local; 2. The influence of the environment on the particle X-t is small; 3. The particle modifies the environment of its location (it cancels the memory of the environment). We consider a large deviation problem for the random walk X-t, t epsilon Z(+). We prove that a large deviation principle holds for this random walk with a good rate function which is analytic with respect to the parameter of interaction in a neighborhood of 0. (C) Elsevier, Paris.