A problem on large deviations in a space of trajectories

The paper deals with the probabilities of large deviations of the trajectories generated by the sums of independent identically distributed random variables with finite moments of the order greater than 2. No restrictions on the character of deviations are assumed.
For the case when the tail probabilities of summands change regularly we derive some results on the asymptotical behaviour of the probabilities of large deviations of trajectories.