Large deviation principles for the finite-dimensional distributions of compound renewal processes

The paper deals with the large deviation probabilities for compound renewal processes. We establish the local and “integral” principles of large deviations in the state space of the process (i.e. for the value of the process at time $T$ as $T\to\infty$). We also find conditions for asymptotically weak dependence of the increments of the processes (in the crude asymptotics sense) and prove the local and “integral” principles of large deviations for the finite-dimensional distributions of the process.