Precise large deviations for dependent random variables with heavy tails

By Li Liu. 2009

334 citations recorded by the source corpus.

Subfields: Finance, Management Science and Operations Research, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/a0fc18eb769e650de9e4cb8a538f9ca2ad2d7a6d

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In Finance

1. Aiting Shen
2. Shuhe Hu
3. Xuejun Wang
4. Yuebao Wang
5. Andrei Volodin
6. Chen Xu
7. Lulu Zheng
8. D. Qiu

In Management Science and Operations Research

1. Aiting Shen
2. Xuejun Wang
3. Shuhe Hu
4. Andrei Volodin
5. Chen Xu
6. Yuebao Wang
7. Kaiyong Wang
8. Yiqing Chen

In Mathematical Physics

1. Aiting Shen
2. Yiqing Chen
3. Kam Chuen Yuen
4. Shuhe Hu
5. Xuejun Wang
6. Li-Xin Zhang
7. Qingwu Gao
8. Yuebao Wang

Citations in the corpus

• Probability inequalities for END sequence and their applications (2011, background): “See, for example, Liu [4] obtained the precise large deviations for dependent random variables with heavy tails.”
• Bernstein-Type Inequality for Widely Dependent Sequence and Its Application to Nonparametric Regression Models (2013, background): “The concept of general extended negative dependence was proposed by Liu [31, 32] and further promoted by Chen et al. [33, 34], Shen [35],Wang andChen [18], S. J.Wang and W. S. Wang [36] and Wang et al. [37], and so forth.”
• Strong limit theorems for extended independent and extended negatively dependent random variables under non-linear expectations (2016, background): “…xi} ) ≤ K n∏ i=1 P (Yi ≤ xi) , ∀ n, (2.4) and they are called upper extended negatively dependent (UEND) if for all xi, i = 1, 2, . . ., P ( n⋂ i=k=1 {Yi > xi} ) ≤ K n∏ i=1 P (Yi > xi) , ∀ n. (2.5) They are called extended negatively dependent (END) if they are both LEND and UEND (cf., Liu (2009)).”
• Uniform Asymptotics for the Finite-Time Ruin Probability of a Dependent Risk Model with a Constant Interest Rate (2013, background): “Liu 2009 ). So the WUOD and WLOD structures allow some common negatively dependent r.v.s and they also allow some positively dependent r.v.s.”
• On complete convergence for widely orthant-dependent random variables and its applications in nonparametric regression models (2014, background): “The concept of general extended negative dependence was proposed by Liu (2009), Liu (2010) and further promoted by Chen et al. (2010), Chen et al. (2011), Shen (2011), Shen (2013a), Wang and Cheng (2011), Wang and Wang (2012), and so forth.”
• Complete convergence for weighted sums of END random variables and its application to nonparametric regression models (2016, background): “The concept of END structure was introduced by Liu (2009).”
• Complete and complete moment convergence for weighted sums of widely orthant dependent random variables (2014, background): “[4], Liu [13, 14], Yang and Wang [26], and so on.”
• On the complete convergence for arrays of rowwise extended negatively dependent random variables (2013, methodology): “Liu ([11]) introduced the following dependence structure.”
• Complete consistency for the estimator of nonparametric regression models based on extended negatively dependent errors (2015, background): “The concept of END sequence was introduced by Liu.[1] In the case M = 1, the notion of END random variables reduces to the well-known notion of so-called negatively dependent (ND) random variables which was introduced by Lehmann [2] (cf.”
• Precise Large Deviations of Random Sums in Presence of Negative Dependence and Consistent Variation (2011, background): “Lemma 3.1 of Liu (2009) , we obtain, respectively,”
• The Strong Law of Large Numbers for Extended Negatively Dependent Random Variables (2010, background): “As a natural generalization of negative dependence, the concept of END was proposed in Liu (2009) and further promoted in Chen et al. (2010) in the study of precise large deviations.”
• Complete convergence and complete moment convergence for arrays of rowwise END random variables (2014, positive): “The concept of extended negatively dependent (END) random variables was introduced by Liu ([11]).”
• Exponential probability inequalities for WNOD random variables and their applications (2016, background): “For the details about the concept and the probability limit theory of END sequence, one can refer to Liu [9], Chen et al.”
• On Complete Convergence for an Extended Negatively Dependent Sequence (2014, background): “The concept of END sequence was introduced by Liu (2009).”