@unpublished{ConfortiRoelly2015,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{ConfortiRoelly2017,
  author    = {Conforti, Giovanni and Roelly, Sylvie},
  title     = {Bridge mixtures of random walks on an Abelian group},
  series = {Bernoulli : official journal of the Bernoulli Society for Mathematical Statistics and Probability},
  volume    = {23},
  journal   = {Bernoulli : official journal of the Bernoulli Society for Mathematical Statistics and Probability},
  publisher = {International Statistical Institute},
  address   = {Voorburg},
  issn      = {1350-7265},
  doi       = {10.3150/15-BEJ783},
  pages     = {1518 -- 1537},
  year      = {2017},
  language  = {en}
}
@misc{RoellyThieullen2005,
  author    = {Roelly, Sylvie and Thieullen, Mich{\`e}le},
  title     = {Duality formula for the bridges of a Brownian diffusion : application to gradient drifts},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-6710},
  year      = {2005},
  abstract  = {In this paper, we consider families of time Markov fields (or reciprocal classes) which have the same bridges as a Brownian diffusion. We characterize each class as the set of solutions of an integration by parts formula on the space of continuous paths C[0; 1]; R-d) Our techniques provide a characterization of gradient diffusions by a duality formula and, in case of reversibility, a generalization of a result of Kolmogorov.},
  language  = {en}
}