Asymptotic tail behavior of a random sum with conditionally dependent subexponential summands

2016 ◽  
Vol 46 (12) ◽  
pp. 5888-5895 ◽  
Author(s):  
Yanfang Zhang ◽  
Fengyang Cheng
Keyword(s):  
Random Sum ◽  
Tail Behavior ◽  
Asymptotic Tail

scholarly journals Multiperiod conditional distribution functions for conditionally normal GARCH(1, 1) models

2005 ◽  
Vol 42 (02) ◽  
pp. 426-445
Author(s):  
Raymond Brummelhuis ◽  
Dominique Guégan
Keyword(s):  
Conditional Probability ◽  
Conditional Distribution ◽  
Probability Distributions ◽  
Random Variables ◽  
Distribution Functions ◽  
Tail Behavior ◽  
Asymptotic Tail

We study the asymptotic tail behavior of the conditional probability distributions of r t+k and r t+1+⋯+r t+k when (r t ) t∈ℕ is a GARCH(1, 1) process. As an application, we examine the relation between the extreme lower quantiles of these random variables.

Tests of elliptical symmetry and the asymptotic tail behavior of the statistics

1999 ◽  
Vol 14 (4) ◽  
pp. 423-432
Author(s):  
Jing Ping ◽  
Zhu Lixing
Keyword(s):  
Tail Behavior ◽  
Elliptical Symmetry ◽  
Asymptotic Tail

scholarly journals First-passage time asymptotics over moving boundaries for random walk bridges

2018 ◽  
Vol 55 (2) ◽  
pp. 627-651 ◽  
Author(s):  
Fiona Sloothaak ◽  
Vitali Wachtel ◽  
Bert Zwart
Keyword(s):  
Random Walk ◽  
Moving Boundary ◽  
First Passage Time ◽  
Passage Time ◽  
Finite Variance ◽  
Tail Behavior ◽  
First Passage ◽  
The Impact ◽  
Return Point ◽  
Asymptotic Tail

Abstract We study the asymptotic tail behavior of the first-passage time over a moving boundary for a random walk conditioned to return to zero, where the increments of the random walk have finite variance. Typically, the asymptotic tail behavior may be described through a regularly varying function with exponent -½, where the impact of the boundary is captured by the slowly varying function. Yet, the moving boundary may have a stronger effect when the tail is considered at a time close to the return point of the random walk bridge, leading to a possible phase transition depending on the order of the distance between zero and the moving boundary.

scholarly journals Multiperiod conditional distribution functions for conditionally normal GARCH(1, 1) models

2005 ◽  
Vol 42 (2) ◽  
pp. 426-445 ◽  
Author(s):  
Raymond Brummelhuis ◽  
Dominique Guégan
Keyword(s):  
Conditional Probability ◽  
Conditional Distribution ◽  
Probability Distributions ◽  
Random Variables ◽  
Distribution Functions ◽  
Tail Behavior ◽  
Asymptotic Tail

We study the asymptotic tail behavior of the conditional probability distributions of rt+k and rt+1+⋯+rt+k when (rt)t∈ℕ is a GARCH(1, 1) process. As an application, we examine the relation between the extreme lower quantiles of these random variables.

scholarly journals Tail behavior of negatively associated heavy-tailed sums

2006 ◽  
Vol 43 (02) ◽  
pp. 587-593 ◽  
Author(s):  
Jaap Geluk ◽  
Kai W. Ng
Keyword(s):  
Random Variables ◽  
Distribution Functions ◽  
Subexponential Distribution ◽  
Tail Behavior ◽  
Tail Probabilities ◽  
Negatively Associated ◽  
Class D ◽  
Dominatedly Varying Tails ◽  
Heavy Tailed ◽  
Asymptotic Tail

Consider a sequence {X k , k ≥ 1} of random variables on (−∞, ∞). Results on the asymptotic tail probabilities of the quantities , and S (n) = max0 ≤ k ≤ n S k , with X 0 = 0 and n ≥ 1, are well known in the case where the random variables are independent with a heavy-tailed (subexponential) distribution. In this paper we investigate the validity of these results under more general assumptions. We consider extensions under the assumptions of having long-tailed distributions (the class L) and having the class D ∩ L, where D is the class of distribution functions with dominatedly varying tails. Some results are also given in the case where X k , k ≥ 1, are not necessarily identically distributed and/or independent.

scholarly journals Sums of Dependent Nonnegative Random Variables with Subexponential Tails

2008 ◽  
Vol 45 (1) ◽  
pp. 85-94 ◽  
Author(s):  
Bangwon Ko ◽  
Qihe Tang
Keyword(s):  
Random Variables ◽  
Tail Behavior ◽  
Tail Probabilities ◽  
The Impact ◽  
Asymptotic Tail

In this paper we study the asymptotic tail probabilities of sums of subexponential, nonnegative random variables, which are dependent according to certain general structures with tail independence. The results show that the subexponentiality of the summands eliminates the impact of the dependence on the tail behavior of the sums.

scholarly journals Tail behavior of negatively associated heavy-tailed sums

2006 ◽  
Vol 43 (2) ◽  
pp. 587-593 ◽  
Author(s):  
Jaap Geluk ◽  
Kai W. Ng
Keyword(s):  
Random Variables ◽  
Distribution Functions ◽  
Subexponential Distribution ◽  
Tail Behavior ◽  
Tail Probabilities ◽  
Negatively Associated ◽  
Class D ◽  
Dominatedly Varying Tails ◽  
Heavy Tailed ◽  
Asymptotic Tail

Consider a sequence {Xk, k ≥ 1} of random variables on (−∞, ∞). Results on the asymptotic tail probabilities of the quantities , and S(n) = max0 ≤ k ≤ nSk, with X0 = 0 and n ≥ 1, are well known in the case where the random variables are independent with a heavy-tailed (subexponential) distribution. In this paper we investigate the validity of these results under more general assumptions. We consider extensions under the assumptions of having long-tailed distributions (the class L) and having the class D ∩ L, where D is the class of distribution functions with dominatedly varying tails. Some results are also given in the case where Xk, k ≥ 1, are not necessarily identically distributed and/or independent.

scholarly journals Sums of Dependent Nonnegative Random Variables with Subexponential Tails

2008 ◽  
Vol 45 (01) ◽  
pp. 85-94 ◽  
Author(s):  
Bangwon Ko ◽  
Qihe Tang
Keyword(s):  
Random Variables ◽  
Tail Behavior ◽  
Tail Probabilities ◽  
The Impact ◽  
Asymptotic Tail

In this paper we study the asymptotic tail probabilities of sums of subexponential, nonnegative random variables, which are dependent according to certain general structures with tail independence. The results show that the subexponentiality of the summands eliminates the impact of the dependence on the tail behavior of the sums.

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