Modelling extremal events: for insurance and finance
Modelling extremal events: for insurance and finance
UNIFORM ESTIMATES FOR THE TAIL PROBABILITY OF MAXIMA OVER FINITE HORIZONS WITH SUBEXPONENTIAL TAILS
Probability in the Engineering and Informational Sciences
Heavy Tails in Multi-Server Queue
Queueing Systems: Theory and Applications
On Sums of Conditionally Independent Subexponential Random Variables
Mathematics of Operations Research
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We consider the sums Sn=ξ1+⋅⋅⋅+ξn of independent identically distributed random variables. We do not assume that the ξ's have a finite mean. Under subexponential type conditions on distribution of the summands, we find the asymptotics of the probability P{Mx} as x→∞, provided that M=sup {Sn,n⩾1} is a proper random variable. Special attention is paid to the case of tails which are regularly varying at infinity. We provide some sufficient conditions for the integrated weighted tail distribution to be subexponential. We supplement these conditions by a number of examples which cover both the infinite- and the finite-mean cases. In particular, we show that the subexponentiality of distribution F does not imply the subexponentiality of its integrated tail distribution FI.