TY  - JOUR
A1  - Murr, Rüdiger
T1  - Characterization of infinite divisibility by duality formulas  application to Levy processes and random measures
JF  - Stochastic processes and their application
N2  - Processes with independent increments are proven to be the unique solutions of duality formulas. This result is based on a simple characterization of infinitely divisible random vectors by a functional equation in which a difference operator appears. This operator is constructed by a variational method and compared to approaches involving chaos decompositions. We also obtain a related characterization of infinitely divisible random measures.
KW  - Duality formula
KW  - Integration by parts formula
KW  - Malliavin calculus
KW  - Infinite divisibility
KW  - Levy processes
KW  - Random measures
Y1  - 2013
U6  - https://doi.org/10.1016/j.spa.2012.12.012
SN  - 0304-4149
VL  - 123
IS  - 5
SP  - 1729
EP  - 1749
PB  - Elsevier
CY  - Amsterdam
ER  -