@article{ConfortiLeonardMurretal.2015,
  author    = {Conforti, Giovanni and Leonard, Christian and Murr, R{\"u}diger and Roelly, Sylvie},
  title     = {Bridges of Markov counting processes. Reciprocal classes and duality formulas},
  series = {Electronic communications in probability},
  volume    = {20},
  journal   = {Electronic communications in probability},
  publisher = {Univ. of Washington, Mathematics Dep.},
  address   = {Seattle},
  issn      = {1083-589X},
  doi       = {10.1214/ECP.v20-3697},
  pages     = {12},
  year      = {2015},
  abstract  = {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.},
  language  = {en}
}
@article{Murr2013,
  author    = {Murr, R{\"u}diger},
  title     = {Characterization of infinite divisibility by duality formulas application to Levy processes and random measures},
  series = {Stochastic processes and their application},
  volume    = {123},
  journal   = {Stochastic processes and their application},
  number    = {5},
  publisher = {Elsevier},
  address   = {Amsterdam},
  issn      = {0304-4149},
  doi       = {10.1016/j.spa.2012.12.012},
  pages     = {1729 -- 1749},
  year      = {2013},
  abstract  = {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.},
  language  = {en}
}