Inequalities and principles of large deviations for the trajectories of processes with independent increments

We consider a homogeneous process S (t) on 0, ∞) with independent increments, establish the local and ordinary large deviation principles for the trajectories of the processes sT (t): = 1 TS (tT), t ∈ [0, 1, as T → ∞, and obtain a series of inequalities for the distributions of the trajectories of S (t).