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Large deviation principles for random walk trajectories. III. (English) Zbl 1293.60035

Theory Probab. Appl. 58, No. 1, 25-37 (2014); translation from Teor. Veroyatn. Primen. 58, No. 1, 37-52 (2013).
Summary: 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.

MSC:

60F10 Large deviations
60G50 Sums of independent random variables; random walks

Citations:

Zbl 1279.60037
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