@article{ConfortiPraRoelly2015,
  author    = {Conforti, Giovanni and Pra, Paolo Dai and Roelly, Sylvie},
  title     = {Reciprocal Class of Jump Processes},
  series = {Journal of theoretical probability},
  volume    = {30},
  journal   = {Journal of theoretical probability},
  publisher = {Springer},
  address   = {New York},
  issn      = {0894-9840},
  doi       = {10.1007/s10959-015-0655-3},
  pages     = {551 -- 580},
  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 compound Poisson processes whose jumps belong to a finite set . We propose a characterization of the reciprocal class as the unique set of probability measures on which a family of time and space transformations induces the same density, expressed in terms of the reciprocal invariants. The geometry of plays a crucial role in the design of the transformations, and we use tools from discrete geometry to obtain an optimal characterization. We deduce explicit conditions for two Markov jump processes to belong to the same class. Finally, we provide a natural interpretation of the invariants as short-time asymptotics for the probability that the reference process makes a cycle around its current state.},
  language  = {en}
}
@article{ConfortiKosenkovaRoelly2019,
  author    = {Conforti, Giovanni and Kosenkova, Tetiana and Roelly, Sylvie},
  title     = {Conditioned Point Processes with Application to Levy Bridges},
  series = {Journal of theoretical probability},
  volume    = {32},
  journal   = {Journal of theoretical probability},
  number    = {4},
  publisher = {Springer},
  address   = {New York},
  issn      = {0894-9840},
  doi       = {10.1007/s10959-018-0863-8},
  pages     = {2111 -- 2134},
  year      = {2019},
  abstract  = {Our first result concerns a characterization by means of a functional equation of Poisson point processes conditioned by the value of their first moment. It leads to a generalized version of Mecke's formula. En passant, it also allows us to gain quantitative results about stochastic domination for Poisson point processes under linear constraints. Since bridges of a pure jump L{\´e}vy process in Rd with a height a can be interpreted as a Poisson point process on space-time conditioned by pinning its first moment to a, our approach allows us to characterize bridges of L{\´e}vy processes by means of a functional equation. The latter result has two direct applications: First, we obtain a constructive and simple way to sample L{\´e}vy bridge dynamics; second, it allows us to estimate the number of jumps for such bridges. We finally show that our method remains valid for linearly perturbed L{\´e}vy processes like periodic Ornstein-Uhlenbeck processes driven by L{\´e}vy noise.},
  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}
}
@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}
}