Lévy Processes in Cones of Banach Spaces

Abstract

Subordinators in Banach spaces are studied. The existence of the special Lévy-Khintchine representation is related to the geometry of the space and a Pettis integral with respect to the underlying Lévy measure. Rates of growth of subordinators in a special type of Banach spaces are studied, including laws of iterated logarithm which give new results in finite dimensions bigger than one.