Abstract:
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 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.
Citation:
A. A. Borovkov, A. A. Mogulskii, “Large deviation principles for random walk trajectories. III”, Teor. Veroyatnost. i Primenen., 58:1 (2013), 37–52; Theory Probab. Appl., 58:1 (2014), 25–37
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