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On the theory of large deviations. (English. Russian original) Zbl 0807.60036
Theory Probab. Appl. 38, No. 3, 490-497 (1993); translation from Teor. Veroyatn. Primen. 38, No. 3, 553-562 (1993).
Summary: The similarity of the “large deviation principle, (DV1) and (DV2)” and the “weak convergence of probability measures” was used by the author in the earlier paper [in: New trends in probability and statistics. Vol. 1, Proc. 23rd Bakuriani Colloq. in Honour of Yu. V. Prokhorov, Bakuriani/USSR 1990, 198-218 (1991; Zbl 0767.60024)] to study the rough asymptotic behavior of large deviations by the techniques of the theory of weak convergence. A simpler proof is given for one of the main results of the paper quoted above (“if a sequence of measures is exponentially tight, then it is relatively compact in the sense of large deviations”). The problem of large deviations for semimartingales is considered.

60F10 Large deviations
60G48 Generalizations of martingales