Second-order subexponential behavior of subordinated sequences

Abstract:

Suppose that {a(n), n ε N 0 }, {b(n), n ε N 0 }, and {p(n), n ε N 0 } are three discrete probability distributions related by the equation (E): b(n) = ∑ k=0∞ p(k)a *k (n), where {a *k (n), n ε N 0 } denotes the k-fold convolution of {a(n), n ε N 0 }. In this paper, we investigate the relation between the asymptotic behaviors of a and b. It turns out that, for wide classes of sequences a and p, relation (E) implies that b(n)/a(n) → EN, where EN is the mean of p. The main object of this paper is to discuss the rate of convergence in this result. In our main results, we obtain O-estimates and exact asymptotic estimates for the difference b(n) - ENa(n).

Año de publicación:

2003

Keywords:

• Subordinate sequences
• Subexponential sequences
• Random walk

Fuente:

scopus