Asymptotic results for random walks in continuous time with alternating rates

We investigate some large deviation problems for a random walk in continuous time {N(t);t≥0} with spatially inhomogeneous rates of alternating type. We first deal with the large deviation principle for the convergence of N(t)/t to a suitable constant. Then, the case of moderate deviations is also discussed. Motivated by possible applications in chemical physics context, we finally obtain an asymptotic lower bound for level crossing probabilities both in the case of finite and infinite horizon.