منابع مشابه
Limit theorems for sums of random exponentials
Received: date / Revised version: date Abstract. We study limiting distributions of exponential sums SN (t) = ∑N i=1 e tXi as t → ∞, N → ∞, where (Xi) are i.i.d. random variables. Two cases are considered: (A) ess supXi = 0 and (B) ess supXi = ∞. We assume that the function h(x) = − log P{Xi > x} (case B) or h(x) = − log P{Xi > −1/x} (case A) is regularly varying at ∞ with index 1 < % < ∞ (case...
متن کاملLimit Laws for Sums of Random Exponentials
We study the limiting distribution of the sum SN (t) = PN i=1 e tXi as t → ∞, N → ∞, where (Xi) are i.i.d. random variables. Attention to such exponential sums has been motivated by various problems in random media theory. Examples include the quenched mean population size of a colony of branching processes with random branching rates and the partition function of Derrida’s Random Energy Model....
متن کاملStrong limit theorems for partial sums of a random sequence
Let {ξj ; j ≥ 1} be a centered strictly stationary random sequence defined by S0 = 0, Sn = ∑n j=1 ξj and σ(n) = √ ES2 n, where σ(t), t > 0, is a nondecreasing continuous regularly varying function. Suppose that there exists n0 ≥ 1 such that, for any n ≥ n0 and 0 ≤ ε < 1, there exist positive constants c1 and c2 such that c1 e−(1+ε)x 2/2 ≤ P { |Sn| σ(n) ≥ x } ≤ c2 e −(1−ε)x2/2, x ≥ 1. Under some...
متن کاملLimit theorems for sums of random variables with mixture distribution
In this paper, we study the fluctuations of sums of random variables with distribution defined as a mixture of light-tail and truncated heavy-tail distributions. We focus on the case when both the mixing coefficient and the truncation level depend on the number of summands. The aim of this research is to characterize the limiting distributions of the sums due to various relations between these ...
متن کاملConditioned Limit Theorems for Weighted Sums of Random Sequence
Some notions of conditionally dominated random variables are introduced and characterized, Under rather minimal assumptions on random variables {X,Xn, n ≥ 1}, some limit theorems of Jamison’s type of weighted sums of random variables are obtained. Mathematics Subject Classification: 60F15
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ژورنال
عنوان ژورنال: Probability Theory and Related Fields
سال: 2005
ISSN: 0178-8051,1432-2064
DOI: 10.1007/s00440-004-0406-3