@unpublished{ConfortiRoelly2015,
  author    = {Conforti, Giovanni and Roelly, Sylvie},
  title     = {Reciprocal class of random walks on an Abelian group},
  volume    = {4},
  number    = {1},
  publisher = {Universit{\"a}tsverlag Potsdam},
  address   = {Potsdam},
  issn      = {2193-6943},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-72604},
  pages     = {22},
  year      = {2015},
  abstract  = {Processes having the same bridges as a given reference Markov process constitute its reciprocal class. In this paper we study the reciprocal class of a continuous time random walk with values in a countable Abelian group, we compute explicitly its reciprocal characteristics and we present an integral characterization of it. Our main tool is a new iterated version of the celebrated Mecke's formula from the point process theory, which allows us to study, as transformation on the path space, the addition of random loops. Thanks to the lattice structure of the set of loops, we even obtain a sharp characterization. At the end, we discuss several examples to illustrate the richness of reciprocal classes. We observe how their structure depends on the algebraic properties of the underlying group.},
  language  = {en}
}
@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}
}