Geodesic
On the theory of large deviations
Teoriâ veroâtnostej i ee primeneniâ, Tome 38 (1993) no. 3, pp. 553-562

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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 [9] to study the rough asymptotic behavior of large deviations by the techniques of the theory of weak convergence. This paper is a continuation of [9]. A simpler proof is given for one of the main results of [9] (“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.
Keywords: rough asymptotic behavior of large deviations, weak convergence tightness of probability measures, Prokhorov's theorem, rate function, large deviations for semimartingales. 
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     title = {On the theory of large deviations},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
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A. A. Pukhal'skii. On the theory of large deviations. Teoriâ veroâtnostej i ee primeneniâ, Tome 38 (1993) no. 3, pp. 553-562. http://geodesic.mathdoc.fr/item/TVP_1993_38_3_a5/