New results on the order of functions at infinity

Meitner Cadena (1) , Marie Kratz (2) , Edward Omey (3)

1 Universidad de las Fuerzas Armadas
2 ESSEC Business School
3 KU Leuven - Catholic University of Leuven = Katholieke Universiteit Leuven

Recently, new classes of positive and measurable functions, M(ρ) and M(±∞), have been defined in terms of their asymptotic behaviour at infinity, when normalized by a logarithm (Cadena et al., 2015, 2016, 2017). Looking for other suitable normalizing functions than logarithm seems quite natural. It is what is developed in this paper, studying new classes of functions of the type lim x→∞ log U (x)/H(x) = ρ < ∞ for a large class of normalizing functions H. It provides subclasses of M(0) and M(±∞).

Mots clés: functions at infinity

Domaines: Probabilités [math.PR]; Économie et finance quantitative [q-fin]

Meitner Cadena, Marie Kratz, Edward Omey. New results on the order of functions at infinity. 2017. ⟨hal-01558855⟩