 Approximation of the tail probability of randomly weighted sums and applicationsYi Zhang, Xinmei Shen and Chengguo Weng Stochastic Processes and their Applications, 2009, vol. 119, issue 2, 655-675 Abstract: Consider the problem of approximating the tail probability of randomly weighted sums and their maxima, where {Xi,i>=1} is a sequence of identically distributed but not necessarily independent random variables from the extended regular variation class, and {[Theta]i,i>=1} is a sequence of nonnegative random variables, independent of {Xi,i>=1} and satisfying certain moment conditions. Under the assumption that {Xi,i>=1} has no bivariate upper tail dependence along with some other mild conditions, this paper establishes the following asymptotic relations: and as x-->[infinity]. In doing so, no assumption is made on the dependence structure of the sequence {[Theta]i,i>=1}. Keywords: Randomly; weighted; sums; Asymptotics; Regular; variation; Upper; tail; dependence; Ruin; probability; Stochastic; difference; equations (search for similar items in EconPapers) Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:eee:spapps:v:119:y:2009:i:2:p:655-675 Ordering information: This journal article can be ordered from Access Statistics for this article Stochastic Processes and their Applications is currently edited by T. Mikosch More articles in Stochastic Processes and their Applications from Elsevier |
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