N ov 2 00 7 Lower limits for distributions of randomly stopped sums

ar X iv : m at h . PR / 0 70 19 20 v 2 21 F eb 2 00 7 On lower limits and equivalences for distribution tails of randomly stopped sums

For a distribution F * τ of a random sum S τ = ξ 1 +. .. + ξ τ 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 F * τ (x)/F (x) as x → ∞ (here τ is an independent counting random variable). We also consider applications of obtained results to random walks, compound Poisson distributions, infinitely divisible laws, and su...

1 7 N ov 2 00 4 Cosine Products , Fourier Transforms , and Random Sums ∗

. PR ] 2 1 Fe b 20 07 On lower limits and equivalences for distribution tails of randomly stopped sums

For a distribution F * τ of a random sum S τ = ξ 1 +. .. + ξ τ 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 F * τ (x)/F (x) as x → ∞ (here τ is an independent counting random variable). We also consider applications of obtained results to random walks, compound Poisson distributions, infinitely divisible laws, and su...

m at h . PR ] 3 1 Ja n 20 07 On lower limits and equivalences for distribution tails of randomly stopped sums

For a distribution F * τ of a random sum S τ = ξ 1 +. .. + ξ τ 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 F * τ (x)/F (x) as x → ∞ (here τ is an independent counting random variable). We also consider applications of obtained results to random walks, compound Poisson distributions, infinitely divisible laws, and su...

1 9 N ov 2 00 4 Power Sums Related to Semigroups S ( d 1 , d 2 , d 3 )

The explicit formulas for the sums of positive powers of the integers si unrepresentable by the triple of integers d1, d2, d3 ∈ N, gcd(d1, d2, d3) = 1, are derived.