On lower limits and equivalences for distribution tails of randomly stopped sums
Denisov, Denis ; Foss, Serguei ; Korshunov, Dmitry
Bernoulli, Tome 14 (2008) no. 1, p. 391-404 / Harvested from Project Euclid
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For a distribution F*τ of a random sum Sτ=ξ1+⋯+ξτ of i.i.d. random variables with a common distribution F on the half-line [0, ∞), we study the limits of the ratios of tails $\overline{F^{*\tau}}(x)/\overline{F}(x)$ as x→∞ (here, τ is a counting random variable which does not depend on {ξn}n≥1). We also consider applications of the results obtained to random walks, compound Poisson distributions, infinitely divisible laws, and subcritical branching processes.
Publié le : 2008-05-15
Classification:  convolution tail,  convolution equivalence,  lower limit,  randomly stopped sums,  subexponential distribution 
@article{1208872110,
     author = {Denisov, Denis and Foss, Serguei and Korshunov, Dmitry},
     title = {On lower limits and equivalences for distribution tails of randomly stopped sums},
     journal = {Bernoulli},
     volume = {14},
     number = {1},
     year = {2008},
     pages = { 391-404},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1208872110}
}

Denisov, Denis; Foss, Serguei; Korshunov, Dmitry. On lower limits and equivalences for distribution tails of randomly stopped sums. Bernoulli, Tome 14 (2008) no. 1, pp.  391-404. http://gdmltest.u-ga.fr/item/1208872110/