Second-order subexponential sequences and the asymptotic behavior of their de pril transform

Abstract:

Suppose that {f(w), n ∈ N0} is a sequence of positive real numbers and suppose that the sequence (a(n), n ∈ N0} is given by a(0) = 0, and, for n ≥ 1, by the convolution equation nf(n) = a * f(n). The resulting sequence is denoted by a(n) = φf(n) and is called the De Pril transform of {f(n), n ∈ N0}. In this paper, we consider first- and second-order asymptotic behavior of {φf(n), n ∈ N0} for a large class of subexponential sequences {φf(n), n ∈ N0}. We also discuss some applications. © 2001 Plenum Publishing Corporation.

Año de publicación:

2001

Keywords:

• O-regular variation
• Random walk
• Subexponential sequences
• De Pril transform
• Harmonic renewal sequence

Fuente:

scopus