Release Time:2019-03-12  Hits:

Indexed by: Journal Article

Date of Publication: 2017-06-01

Journal: FRONTIERS OF MATHEMATICS IN CHINA

Included Journals: Scopus、SCIE

Volume: 12

Issue: 3

Page Number: 711-732

ISSN: 1673-3452

Key Words: Precise large deviations; multi-dimensional; consistently varying distributions; random sums

Abstract: Let {X (i) = (X (1,i) ,...,X (m,i) )(aS<currency>), i 1} be a sequence of independent and identically distributed nonnegative m-dimensional random vectors. The univariate marginal distributions of these vectors have consistently varying tails and finite means. Here, the components of X (1) are allowed to be generally dependent. Moreover, let N(center dot) be a nonnegative integer-valued process, independent of the sequence {X (i) , i 1}. Under several mild assumptions, precise large deviations for S (n) = I  pound (i=1) (n) X (i) and S (N(t)) = I  pound (i=1) (N(t)) X (i) are investigated. Meanwhile, some simulation examples are also given to illustrate the results.