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  - 
TY  - JOUR
A1  - Conforti, Giovanni
A1  - Leonard, Christian
A1  - Murr, Rüdiger
A1  - Roelly, Sylvie
T1  - Bridges of Markov counting processes. Reciprocal classes and duality formulas
JF  - Electronic communications in probability
N2  - Processes sharing the same bridges are said to belong to the same reciprocal class. In this article we analyze reciprocal classes of Markov counting processes by identifying their reciprocal invariants and we characterize them as the set of counting processes satisfying some duality formula.
KW  - Counting process
KW  - bridge
KW  - reciprocal class
KW  - duality formula
Y1  - 2015
U6  - https://doi.org/10.1214/ECP.v20-3697
SN  - 1083-589X
VL  - 20
PB  - Univ. of Washington, Mathematics Dep.
CY  - Seattle
ER  -