Limit theorems for stopped random sequences II: large deviations

Stopped random sequences with record regeneration are considered and upper bounds and approximations of probabilities of large deviations under low moment conditions are obtained. These results generalize those of A. V. Nagaev, S. V. Nagaev, and D. X. Fuk proved in the framework of sums of independent random variables. Particular cases of such sequences are stopped random walks, recurrent Markov renewal processes, and certain procedures of sequential estimation.