Borovkov, A. A.; Mogulskii, A. A. On large deviations of sums of independent random vectors on the boundary and outside of the Cramér zone. II. (English. Russian original) Zbl 1205.60055 Theory Probab. Appl. 53, No. 4, 573-593 (2009); translation from Teor. Veroyatn. Primen. 53, No. 4, 641-664 (2008). Summary: The present paper continues [A. A. Borovkov and A. A. Mogulskii, Theory Probab. Appl. 53, 301–311 (2009; Zbl 1201.60025)] and is devoted to studying the asymptotics of the probability that a sum of independent random vectors falls into a small cube with a vertex at a point \(x\) in the large deviation zone. This asymptotics is found in the multivariate case for a class of distributions regularly varying at infinity and for deviations well beyond the Cramér zone. MSC: 60F10 Large deviations 60G50 Sums of independent random variables; random walks Keywords:deviation function; large deviations; irregular large deviations; Cramér large deviation zone; superlarge deviations; integrolocal theorems Citations:Zbl 1201.60025 PDFBibTeX XMLCite \textit{A. A. Borovkov} and \textit{A. A. Mogulskii}, Theory Probab. Appl. 53, No. 4, 573--593 (2009; Zbl 1205.60055); translation from Teor. Veroyatn. Primen. 53, No. 4, 641--664 (2008) Full Text: DOI