Precise large deviations for sums of random vectors with dependent components of consistently varying tails

doi:10.1007/s11464-017-0635-2

Front. Math. China

2017, Vol. 12

Issue (3) : 711-732 https://doi.org/10.1007/s11464-017-0635-2

RESEARCH ARTICLE

Precise large deviations for sums of random vectors with dependent components of consistently varying tails

Xinmei SHEN(

), Yuqing NIU, Hailan TIAN

School of Mathematical Sciences, Dalian University of Technology, Dalian 116024, China

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Abstract

Let ${X i = (X 1, i, . . ., X m, i) T, i ≥ 1}$ 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 $N (·)$ be a nonnegative integer-valued process, independent of the sequence ${X i, i ≥ 1}$ .Under several mild assumptions, precise large deviations for $S n = ∑ i = 1 n X i$ and $S N (t) = ∑ i = 1 N (t) X i$ are investigated. Meanwhile, some simulation examples are also given to illustrate the results.

Keywords Precise large deviations multi-dimensional consistently varying distributions random sums

Corresponding Author(s): Xinmei SHEN

Issue Date: 20 April 2017

Cite this article:

Xinmei SHEN,Yuqing NIU,Hailan TIAN. Precise large deviations for sums of random vectors with dependent components of consistently varying tails[J]. Front. Math. China, 2017, 12(3): 711-732.

URL:

https://academic.hep.com.cn/fmc/EN/10.1007/s11464-017-0635-2
https://academic.hep.com.cn/fmc/EN/Y2017/V12/I3/711

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