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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.

MSC:
60F10 Large deviations
60G48 Generalizations of martingales
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