Large deviation principles for random walk trajectories. III
Teoriâ veroâtnostej i ee primeneniâ, Tome 58 (2013) no. 1, pp. 37-52
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The present paper is a continuation of [A. A. Borovkov and A. A. Mogulskii, Theory Probab. Appl. 57, No. 1, 1–27 (2013); translation from Teor. Veroyatn. Primen. 57, No. 1, 3–34 (2012; Zbl 1279.60037)]. It consists of two sections. Section 6 presents results similar to those obtained in Sections 4 and 5, but now in the space of functions of bounded variation with metric stronger than that of $\mathbb{D}$. In Section 7 we obtain the so-called conditional large deviation principles for the trajectories of univariate random walks with a localized terminal value of the walk. As a consequence, we prove a version of Sanov’s theorem on large deviations of empirical distributions.
Keywords:
extended large deviation principle in the space of functions of bounded variation; local large deviation principle; integro-local Gnedenko and Stone-Shepp theorems; Sanov theorem; large deviations of empirical distributions.
@article{TVP_2013_58_1_a3,
author = {A. A. Borovkov and A. A. Mogulskii},
title = {Large deviation principles for random walk trajectories. {III}},
journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
pages = {37--52},
publisher = {mathdoc},
volume = {58},
number = {1},
year = {2013},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TVP_2013_58_1_a3/}
}
TY - JOUR AU - A. A. Borovkov AU - A. A. Mogulskii TI - Large deviation principles for random walk trajectories. III JO - Teoriâ veroâtnostej i ee primeneniâ PY - 2013 SP - 37 EP - 52 VL - 58 IS - 1 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/TVP_2013_58_1_a3/ LA - ru ID - TVP_2013_58_1_a3 ER -
A. A. Borovkov; A. A. Mogulskii. Large deviation principles for random walk trajectories. III. Teoriâ veroâtnostej i ee primeneniâ, Tome 58 (2013) no. 1, pp. 37-52. http://geodesic.mathdoc.fr/item/TVP_2013_58_1_a3/