Borovkov, A. A.; Mogulskii, A. A. 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. Cited in 5 Documents MSC: 60F10 Large deviations 60G50 Sums of independent random variables; random walks 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 Citations:Zbl 1279.60037 PDFBibTeX XMLCite \textit{A. A. Borovkov} and \textit{A. A. Mogulskii}, Theory Probab. Appl. 58, No. 1, 25--37 (2014; Zbl 1293.60035); translation from Teor. Veroyatn. Primen. 58, No. 1, 37--52 (2013) Full Text: DOI