Large Deviations for Partial Sums U-Processes in Dependent Cases

2001 ◽  
Vol 45 (4) ◽  
pp. 569-588
Author(s):  
P. Eichelsbacher
Keyword(s):  
Large Deviations ◽  
Partial Sums

Precise large deviations for sums of random variables with consistently varying tails

2004 ◽  
Vol 41 (01) ◽  
pp. 93-107 ◽  
Author(s):  
Kai W. Ng ◽  
Qihe Tang ◽  
Jia-An Yan ◽  
Hailiang Yang
Keyword(s):  
Large Deviations ◽  
Risk Model ◽  
Random Variables ◽  
Tail Probability ◽  
Arrival Process ◽  
Partial Sums ◽  
Precise Large Deviations ◽  
Sums Of Random Variables ◽  
Doubly Stochastic ◽  
Common Distribution Function

Let {X k , k ≥ 1} be a sequence of independent, identically distributed nonnegative random variables with common distribution function F and finite expectation μ > 0. Under the assumption that the tail probability is consistently varying as x tends to infinity, this paper investigates precise large deviations for both the partial sums S n and the random sums S N(t), where N(·) is a counting process independent of the sequence {X k , k ≥ 1}. The obtained results improve some related classical ones. Applications to a risk model with negatively associated claim occurrences and to a risk model with a doubly stochastic arrival process (extended Cox process) are proposed.

scholarly journals Large deviations for partial sums $U$-processes in dependent cases

2000 ◽  
Vol 45 (4) ◽  
pp. 670-693
Author(s):  
Peter Eichelsbacher ◽  
Peter Eichelsbacher
Keyword(s):  
Large Deviations ◽  
Partial Sums

scholarly journals Precise Large Deviations for Sums of Random Variables with Consistently Varying Tails in Multi-Risk Models

2007 ◽  
Vol 44 (04) ◽  
pp. 889-900 ◽  
Author(s):  
Shijie Wang ◽  
Wensheng Wang
Keyword(s):  
Large Deviations ◽  
Partial Sums ◽  
Counting Processes ◽  
Insurance Company ◽  
Random Sums ◽  
Risk Models ◽  
Precise Large Deviations ◽  
Sums Of Random Variables ◽  
Insurance Contracts ◽  
Claim Number

Assume that there are k types of insurance contracts in an insurance company. The ith related claims are denoted by {X ij , j ≥ 1}, i = 1,…,k. In this paper we investigate large deviations for both partial sums S(k; n 1,…,n k ) = ∑ i=1 k ∑ j=1 n i X ij and random sums S(k; t) = ∑ i=1 k ∑ j=1 N i (t) X ij , where N i (t), i = 1,…,k, are counting processes for the claim number. The obtained results extend some related classical results.

scholarly journals Large deviations principle for partial sums $U$-processes

1998 ◽  
Vol 43 (1) ◽  
pp. 97-115
Author(s):  
Peter Eichelsbacher ◽  
Peter Eichelsbacher ◽  
Matthias Lowe ◽  
Matthias Lowe
Keyword(s):  
Large Deviations ◽  
Partial Sums ◽  
Large Deviations Principle

scholarly journals Precise Large Deviations for Sums of Random Variables with Consistently Varying Tails in Multi-Risk Models

2007 ◽  
Vol 44 (4) ◽  
pp. 889-900 ◽  
Author(s):  
Shijie Wang ◽  
Wensheng Wang
Keyword(s):  
Large Deviations ◽  
Partial Sums ◽  
Counting Processes ◽  
Insurance Company ◽  
Random Sums ◽  
Risk Models ◽  
Precise Large Deviations ◽  
Sums Of Random Variables ◽  
Insurance Contracts ◽  
Claim Number

Assume that there are k types of insurance contracts in an insurance company. The ith related claims are denoted by {Xij, j ≥ 1}, i = 1,…,k. In this paper we investigate large deviations for both partial sums S(k; n1,…,nk) = ∑i=1k ∑j=1niXij and random sums S(k; t) = ∑i=1k ∑j=1Ni (t)Xij, where Ni(t), i = 1,…,k, are counting processes for the claim number. The obtained results extend some related classical results.

Precise large deviations for sums of random variables with consistently varying tails

2004 ◽  
Vol 41 (1) ◽  
pp. 93-107 ◽  
Author(s):  
Kai W. Ng ◽  
Qihe Tang ◽  
Jia-An Yan ◽  
Hailiang Yang
Keyword(s):  
Large Deviations ◽  
Risk Model ◽  
Random Variables ◽  
Tail Probability ◽  
Arrival Process ◽  
Partial Sums ◽  
Precise Large Deviations ◽  
Sums Of Random Variables ◽  
Doubly Stochastic ◽  
Common Distribution Function

Let {Xk, k ≥ 1} be a sequence of independent, identically distributed nonnegative random variables with common distribution function F and finite expectation μ > 0. Under the assumption that the tail probability is consistently varying as x tends to infinity, this paper investigates precise large deviations for both the partial sums Sn and the random sums SN(t), where N(·) is a counting process independent of the sequence {Xk, k ≥ 1}. The obtained results improve some related classical ones. Applications to a risk model with negatively associated claim occurrences and to a risk model with a doubly stochastic arrival process (extended Cox process) are proposed.

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