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.
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/
@article{TVP_1993_38_3_a5,
author = {A. A. Pukhal'skii},
title = {On the theory of large deviations},
journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
pages = {553--562},
year = {1993},
volume = {38},
number = {3},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TVP_1993_38_3_a5/}
}