Rare events of marked finite point processes

We study the rare events of a marked finite point process, where the epochs of the point process are assumed to be the ordered statistics of a finite number of i.i.d. standard uniform random variables, and the marks are assumed to be i.i.d. generally distributed random variables that are themselves independent of the epochs. Under the assumption that the `mark´ random variables are not degenerate at the mean, we derive the large deviations principle satisfied by a ladder process derived from the marked finite point process. The analysis utilizes Varadhan´s Lemma in a non-trivial manner to derive the large deviations result.