A CALCULUS ON LÉVY EXPONENTS AND SELFDECOMPOSABILITY ON
Abstract: In infinite-dimensional Banach spaces there is no complete characterization of the
Lévy exponents of infinitely divisible probability measures. Here we propose a calculus on
Lévy exponents that is derived from some random integrals. As a consequence we prove that
each selfdecomposable measure can by factorized as another selfdecomposable measure and
its background driving measure that is s-selfdecomposable. This complements a result
from the paper of Iksanov, Jurek and Schreiber in the Annals of Probability (2004).
2000 AMS Mathematics Subject Classification: Primary: 60E07, 60B12; Secondary:
Keywords and phrases: Banach space; selfdecomposable; class ; multiply
selfdecomposable; s-selfdecomposable; class ; stable; infinitely divisible; Lévy-Khintchine
formula; Lévy exponent; Lévy process; random integral.