This paper is a further investigation of large deviations for sums of random variables S_n=sum form i=1 to n X_i and S(t)=sum form i=1 to N(t) X_i,(t≥0), where {X_n,n≥1) are independent identically distribution and ...This paper is a further investigation of large deviations for sums of random variables S_n=sum form i=1 to n X_i and S(t)=sum form i=1 to N(t) X_i,(t≥0), where {X_n,n≥1) are independent identically distribution and non-negative random variables, and {N(t),t≥0} is a counting process of non-negative integer-valued random variables, independent of {X_n,n≥1}. In this paper, under the suppose F∈G, which is a bigger heavy-tailed class than C, proved large deviation results for sums of random variables.展开更多
Let X1, X2, ··· be a sequence of dependent and heavy-tailed random variables with distributions F1, F2, ··· on (?∞, ∞), and let τ be a nonnegative integer-valued ran-dom variable indep...Let X1, X2, ··· be a sequence of dependent and heavy-tailed random variables with distributions F1, F2, ··· on (?∞, ∞), and let τ be a nonnegative integer-valued ran-dom variable independent of the sequence {Xk, k ≥ 1}. In this framework, the asymptotic behavior of the tail probabilities of the quantities Sn = n k=1 X k and S(n) = max1 ≤k≤n Sk for n > 1, and their randomized versions Sτ and S(τ) are studied. Some applications to the risk theory are presented.展开更多
文摘This paper is a further investigation of large deviations for sums of random variables S_n=sum form i=1 to n X_i and S(t)=sum form i=1 to N(t) X_i,(t≥0), where {X_n,n≥1) are independent identically distribution and non-negative random variables, and {N(t),t≥0} is a counting process of non-negative integer-valued random variables, independent of {X_n,n≥1}. In this paper, under the suppose F∈G, which is a bigger heavy-tailed class than C, proved large deviation results for sums of random variables.
基金supported by the National Natural Science Foundation of China (No. 11171179)the Research Fund for the Doctoral Program of Higher Education of China (No. 20093705110002)
文摘Let X1, X2, ··· be a sequence of dependent and heavy-tailed random variables with distributions F1, F2, ··· on (?∞, ∞), and let τ be a nonnegative integer-valued ran-dom variable independent of the sequence {Xk, k ≥ 1}. In this framework, the asymptotic behavior of the tail probabilities of the quantities Sn = n k=1 X k and S(n) = max1 ≤k≤n Sk for n > 1, and their randomized versions Sτ and S(τ) are studied. Some applications to the risk theory are presented.
