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Asymptotic Behavior for Random Sums of Negatively Associated Random Variables

Author: ZhangJian
Tutor: ChengFeng
School: Suzhou University
Course: Probability Theory and Mathematical Statistics
Keywords: consistent variation negatively associated random sums asymptotic behavior
CLC: O211
Type: Master's thesis
Year: 2009
Downloads: 7
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Abstract


The random sums of random variables plays an important role in various applied probability fields such as insurance mathematics, queuing theory, teletraffic, etc, and nowadays it has already been studied and referred by an extensive literature. Let {X, Xk : k≥1} be a sequence of random variables, with the common distribution F（x） = 1 - （?）（x） = P（X≤x）. In this paper we focus on the asymptotic behavior of random sums Sτ=∑k=1τXk, whereτis an integer-valued nonnegative random variable independent of {Xk, k≥1}.In 2008, Ale（?）kevi（?）ien（?） et al presented a series of asymptotic relation describing the tail behavior of Sτin which the tail of X is not heavier than ofτ. However under the assumption that X andτis asymptotically equivalent they merely attained an asymptotic upper/lower bound of Sτwhich is far from accomplished. The present paper will step further in this kind of random sums’ tail behavior, to give an equivalent version of asymptotic behavior of Sτin the case X andτis asymptotically equivalent, and extend the result to the negatively associated {X, Xk : k≥1}, finally fulfill the tail behavior of Sτwith an unified outcome.

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CLC: > Mathematical sciences and chemical > Mathematics > Probability Theory and Mathematical Statistics > Theory of probability ( probability theory, probability theory )
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